Calculate voltage, current, resistance, and power for electrical circuits
The calculator will determine the remaining two values using Ohm's Law and Power formulas.
In series circuits, current is the same through all components, but voltage divides across each resistor.
In parallel circuits, voltage is the same across all components, but current divides through each branch.
Decode 4-band or 5-band resistor color codes to determine resistance value and tolerance.
| Color | Digit | Multiplier | Tolerance |
|---|---|---|---|
| Black | 0 | ×1 | - |
| Brown | 1 | ×10 | ±1% |
| Red | 2 | ×100 | ±2% |
| Orange | 3 | ×1K | - |
| Yellow | 4 | ×10K | - |
| Green | 5 | ×100K | ±0.5% |
| Blue | 6 | ×1M | ±0.25% |
| Violet | 7 | ×10M | ±0.1% |
| Gray | 8 | ×100M | ±0.05% |
| White | 9 | ×1G | - |
| Gold | - | ×0.1 | ±5% |
| Silver | - | ×0.01 | ±10% |
Ohm's Law represents one of the most fundamental principles in electrical engineering and electronics, establishing the mathematical relationship between voltage, current, and resistance in electrical circuits. First published by German physicist Georg Simon Ohm in 1827, this elegant formula V = I × R has become the cornerstone of circuit analysis, enabling engineers, electricians, hobbyists, and students to predict circuit behavior, design electrical systems, troubleshoot problems, and ensure safe operation of electrical equipment. Understanding Ohm's Law and its related power equations opens the door to comprehending everything from simple battery-powered LED circuits to complex industrial power distribution systems.
Ohm's Law states that the voltage (V) across a conductor is directly proportional to the current (I) flowing through it, with the constant of proportionality being the resistance (R). Mathematically, this is expressed as V = I × R, where voltage is measured in volts (V), current in amperes or amps (A), and resistance in ohms (Ω). This relationship can be rearranged to solve for any unknown value: I = V / R calculates current when voltage and resistance are known, while R = V / I determines resistance from voltage and current measurements. These three forms of Ohm's Law provide the foundation for analyzing any electrical circuit where resistive elements dominate.
The practical importance of Ohm's Law cannot be overstated. When designing circuits, engineers use Ohm's Law to calculate appropriate resistor values to limit current through LEDs, preventing destruction from excessive current. Electricians apply Ohm's Law to determine wire sizes needed to carry specific currents without overheating, ensuring safe installations that comply with electrical codes. Electronics technicians use Ohm's Law during troubleshooting, measuring voltage and current to identify failed components showing incorrect resistance values. Even automotive mechanics rely on Ohm's Law when diagnosing electrical problems in vehicles, testing circuits to locate shorts, opens, or excessive resistance causing malfunctions.
Beyond basic circuit analysis, Ohm's Law extends to more complex scenarios through series and parallel circuit analysis. In series circuits where components connect end-to-end, the total resistance equals the sum of individual resistances, and the same current flows through all components while voltage divides proportionally. In parallel circuits where components connect across the same two points, voltage remains constant across all branches while current divides according to resistance values, with the total resistance calculated using reciprocal formulas. Understanding these relationships allows designers to create voltage dividers, current dividers, and complex resistor networks that achieve desired electrical characteristics.
Voltage, also called electrical potential difference or electromotive force (EMF), represents the electrical pressure that drives current through a circuit. Measured in volts (V), voltage can be understood through the hydraulic analogy as the pressure that pushes water through pipes. A 9-volt battery provides 9 volts of electrical pressure, while a 120-volt household outlet provides significantly more electrical pressure capable of driving larger currents through the same resistance. Voltage sources include batteries (1.5V for AA/AAA, 9V for 9-volt batteries, 12V for car batteries), USB ports (5V standard, though USB-C can provide higher voltages), household power (120V in North America, 240V in Europe), and industrial power systems (480V three-phase). The voltage level determines how much current can be pushed through a given resistance.
Current, measured in amperes or amps (A), represents the rate of electrical charge flow through a conductor. One ampere equals one coulomb of charge (approximately 6.24 × 10^18 electrons) passing a point per second. Using the hydraulic analogy, current corresponds to the flow rate of water through a pipe. Small currents power electronic devices: a typical LED draws 20 milliamps (0.02A), a smartphone charges at 1-2 amps, while a laptop charger provides 3-5 amps. Household circuits carry larger currents: a 15-amp circuit powers lights and general outlets, 20-amp circuits serve kitchens and bathrooms, and 30-50 amp circuits supply large appliances like electric dryers, ranges, and air conditioners. Industrial equipment may draw hundreds of amperes, requiring heavy cables and specialized overcurrent protection.
Resistance, measured in ohms (Ω), quantifies how much a material opposes current flow. Conductors like copper wire have very low resistance (a few ohms per thousand feet), allowing current to flow easily with minimal voltage drop. Resistors are components specifically designed to provide controlled resistance values, available in standard values from less than one ohm to many megohms (millions of ohms). Insulators like rubber, plastic, and air have extremely high resistance (billions of ohms), preventing current flow except at very high voltages. The resistance of a conductor depends on its material (copper has lower resistance than aluminum or iron), cross-sectional area (thicker wires have less resistance), length (longer conductors have more resistance), and temperature (resistance typically increases with temperature).
The relationship between these three quantities becomes intuitive when considering cause and effect. Voltage is the cause, providing the electrical pressure that drives current. Resistance opposes this pressure, limiting how much current can flow. Current is the effect, the actual flow that results from voltage acting against resistance. Increasing voltage while holding resistance constant increases current proportionally. Increasing resistance while maintaining constant voltage decreases current proportionally. Changing both voltage and resistance affects current according to their ratio. This interdependence means that electrical circuit behavior can always be predicted using Ohm's Law, provided the relationship between voltage and current remains linear (true for resistive circuits but not for components like diodes, transistors, or non-linear loads).
Electrical power, measured in watts (W), represents the rate at which electrical energy is converted to other forms of energy (heat, light, mechanical work, etc.). The fundamental power formula states P = V × I, where power equals voltage multiplied by current. A 120-volt circuit drawing 10 amperes consumes 1,200 watts (1.2 kilowatts) of power. This relationship means that the same power can be delivered at high voltage and low current (more efficient for transmission over long distances) or low voltage and high current (safer for consumer electronics). Understanding power calculations is essential for sizing power supplies, calculating energy costs, and ensuring components don't overheat from excessive power dissipation.
Combining Ohm's Law (V = I × R) with the basic power formula (P = V × I) yields additional useful relationships. Substituting I × R for V gives P = (I × R) × I = I² × R, allowing power calculation from current and resistance alone. Similarly, substituting V / R for I gives P = V × (V / R) = V² / R, enabling power calculation from voltage and resistance. These four power formulas (P = V × I, P = I² × R, P = V² / R, and by rearrangement, P = V² / R) provide flexibility in circuit analysis, allowing power calculation from any two known electrical quantities. Choosing the appropriate formula depends on which parameters are known or can be easily measured.
Power dissipation in resistors is particularly important because all energy flowing through a resistor converts to heat. A 100-ohm resistor carrying 100 milliamps (0.1A) dissipates P = I² × R = 0.1² × 100 = 1 watt of heat. Resistors are rated by both resistance value and maximum power dissipation: common ratings include 1/8 watt (0.125W), 1/4 watt (0.25W), 1/2 watt (0.5W), 1 watt, and higher for power resistors. Operating a resistor beyond its power rating causes overheating, potentially leading to resistance drift, failure, smoke, or fire. Conservative design practice specifies resistors rated for at least twice the expected power dissipation, providing a safety margin for variations in circuit conditions and ensuring longer component life.
Energy consumption calculations extend power concepts to real-world applications. Energy equals power multiplied by time, measured in watt-hours (Wh) or kilowatt-hours (kWh) for practical purposes. A 100-watt light bulb operating for 10 hours consumes 1,000 watt-hours or 1 kilowatt-hour of energy. At typical residential electricity rates of $0.12 per kWh, this costs $0.12. A 1,500-watt space heater running 8 hours daily consumes 12 kWh per day (1.5 kW × 8 hours), costing approximately $1.44 daily or $43 monthly. Understanding these calculations helps evaluate appliance operating costs, size backup power systems (generators, solar panels, battery banks), and make informed decisions about energy-efficient equipment upgrades.
Series circuits connect components end-to-end, creating a single path for current to flow. The defining characteristics of series circuits are that current remains identical through all components, while voltage divides among them according to their resistance values. The total resistance of series circuits equals the sum of individual resistances: R_total = R1 + R2 + R3 + ... This additive property makes series connections useful for increasing total resistance, as in voltage divider circuits, or problematic when unwanted resistance (poor connections, undersized wires) adds to circuit resistance and causes excessive voltage drop.
Voltage division in series circuits follows directly from Ohm's Law. If three resistors of 100Ω, 200Ω, and 300Ω connect in series across a 12-volt supply, total resistance equals 600Ω. Using Ohm's Law, current equals V / R = 12V / 600Ω = 0.02A or 20 milliamps. This same 20mA flows through each resistor. The voltage drop across each resistor equals I × R: the 100Ω resistor drops 2V, the 200Ω resistor drops 4V, and the 300Ω resistor drops 6V. Note that these voltage drops sum to the applied voltage: 2V + 4V + 6V = 12V, confirming Kirchhoff's Voltage Law which states that voltage drops around any closed loop must sum to zero (or equivalently, voltage rises equal voltage drops).
Voltage dividers exploit series circuit behavior to create specific voltage levels from a higher voltage source. A simple voltage divider uses two resistors in series with the output taken from the junction between them. The output voltage equals V_in × R2 / (R1 + R2), where R2 is the resistor connected to ground. For example, dividing 12V to 5V requires R1 and R2 in a ratio where R2 / (R1 + R2) = 5/12. Using standard resistor values, a 470Ω resistor for R1 and a 330Ω resistor for R2 gives V_out = 12V × 330Ω / (470Ω + 330Ω) = 12V × 0.4125 = 4.95V, very close to the desired 5V. Voltage dividers appear extensively in sensor circuits, bias networks, and reference voltage generation.
Series circuits have important limitations. A break anywhere in a series circuit stops all current flow, causing all components to cease functioning. This is why old-style Christmas lights where bulbs connected in series would all go dark if a single bulb failed (modern LED Christmas lights use parallel or series-parallel configurations to avoid this problem). Series circuits also exhibit the problem that adding more loads increases total resistance, reducing current and causing all components to receive less power than intended. These characteristics make series circuits unsuitable for most power distribution applications where independent operation of loads is required, but valuable for specific applications like voltage division, current limiting, and sensing circuits where constant current through all elements is desired.
Parallel circuits connect components across the same two points, creating multiple paths for current flow. The defining characteristics of parallel circuits are that voltage remains identical across all branches, while current divides among them according to their resistance values (or more accurately, conductance values). The total resistance of parallel circuits is always less than the smallest individual resistance, calculated using the reciprocal formula: 1/R_total = 1/R1 + 1/R2 + 1/R3 + ... For two resistors in parallel, this simplifies to R_total = (R1 × R2) / (R1 + R2), often called the "product over sum" formula. This lower total resistance means parallel circuits draw more current than any individual branch.
Current division in parallel circuits follows Ohm's Law applied to each branch independently. If three resistors of 100Ω, 200Ω, and 300Ω connect in parallel across a 12-volt supply, the voltage across each resistor is 12V. Using Ohm's Law for each branch: the 100Ω resistor draws I = V / R = 12V / 100Ω = 0.12A, the 200Ω resistor draws 12V / 200Ω = 0.06A, and the 300Ω resistor draws 12V / 300Ω = 0.04A. The total current from the source equals the sum of branch currents: 0.12A + 0.06A + 0.04A = 0.22A. This confirms Kirchhoff's Current Law which states that current entering a junction equals current leaving that junction, or equivalently, the sum of currents entering a node equals the sum of currents leaving.
The total resistance of this parallel combination can be verified using the reciprocal formula: 1/R_total = 1/100 + 1/200 + 1/300 = 0.01 + 0.005 + 0.00333 = 0.01833. Therefore R_total = 1 / 0.01833 = 54.5Ω. Using Ohm's Law, I = V / R = 12V / 54.5Ω = 0.22A, confirming the current calculated by summing branch currents. Notice that 54.5Ω is indeed less than the smallest individual resistance of 100Ω, demonstrating the characteristic that parallel resistance is always less than the smallest branch resistance.
Parallel circuits dominate practical electrical distribution systems because they allow independent operation of loads. Household electrical wiring uses parallel circuits: all outlets and lights connect in parallel across the 120V supply, so turning off one light doesn't affect others, and the voltage at each outlet remains constant regardless of what's plugged in elsewhere. The current capacity of parallel circuits scales with the number of paths: two identical resistors in parallel carry twice the current of a single resistor at the same voltage, splitting the current equally. This property allows increasing current capacity by paralleling conductors, common in high-current applications where single conductors would be impractically large or inflexible.
Practical parallel circuits must consider the cumulative current draw of all branches. If ten 100Ω loads connect in parallel across 120V, each draws 1.2A, totaling 12A from the source. The circuit breaker and wiring must handle this combined current. This is why household circuits have current ratings (15A, 20A, etc.) and circuit breakers trip when total load exceeds these limits. When designing parallel circuits, calculate the total current by summing all branch currents, then ensure the source, wiring, and overcurrent protection can safely handle this total. Failing to account for cumulative current is a common mistake that leads to overloaded circuits, tripped breakers, overheated wiring, and potential fire hazards.
Through-hole resistors use color bands to indicate their resistance value and tolerance, a system established in the 1920s before digital multimeters made resistance measurement easy. The standard 4-band color code uses the first two bands for significant digits, the third band as a multiplier, and the fourth band for tolerance. For example, a resistor with yellow-violet-red-gold bands reads: yellow = 4, violet = 7, red = ×100, gold = ±5%, indicating 47 × 100 = 4,700Ω or 4.7kΩ with ±5% tolerance (meaning actual resistance is between 4,465Ω and 4,935Ω). The 5-band code used on precision resistors adds a third significant digit before the multiplier, allowing finer resistance values like 147kΩ (brown-yellow-violet-orange-brown).
The color sequence follows the mnemonic "Black Brown Red Orange Yellow Green Blue Violet Gray White" representing digits 0-9. Multiplier colors range from black (×1) through white (×10^9), with gold (×0.1) and silver (×0.01) for resistances below 10Ω. Tolerance colors include gold (±5%), silver (±10%), brown (±1%), red (±2%), green (±0.5%), blue (±0.25%), violet (±0.1%), and gray (±0.05%). No tolerance band indicates ±20%, common on inexpensive carbon composition resistors. Modern metal film resistors typically use brown (±1%) or red (±2%) for general purpose applications, while precision circuits may require 0.1% or 0.05% tolerance resistors.
Resistor power ratings affect physical size: 1/8 watt resistors are tiny (about 3mm long), 1/4 watt resistors are small (about 6mm), 1/2 watt resistors are medium (about 9mm), and larger power resistors (1W, 2W, 5W, 10W, etc.) increase proportionally in size to dissipate more heat. When selecting resistors, calculate expected power dissipation using P = I²R or P = V²/R, then choose a power rating at least 2× higher for reliability. For example, a 1kΩ resistor dropping 10V carries 10mA and dissipates P = V²/R = 100V² / 1000Ω = 0.1W. A 1/4 watt resistor would technically suffice, but a 1/2 watt resistor provides better margin and longer life. In continuous operation or high-temperature environments, even larger derating (3-4×) is prudent.
Modern surface mount resistors use numerical codes rather than color bands. The three-digit code works like the color band system: first two digits are significant figures, third digit is the multiplier exponent. A resistor marked "472" equals 47 × 10² = 4,700Ω = 4.7kΩ. Four-digit codes on precision resistors provide three significant figures plus multiplier: "1002" = 100 × 10² = 10,000Ω = 10kΩ. Very small resistances use "R" to indicate decimal points: "4R7" = 4.7Ω. Surface mount resistors are categorized by size codes (0402, 0603, 0805, 1206, etc.) indicating dimensions in hundredths of inches: an 0805 resistor measures 0.08" × 0.05" or 2.0mm × 1.25mm. Size affects power rating: 0402 typically handle 1/16W, 0603 handle 1/10W, 0805 handle 1/8W, and 1206 handle 1/4W.
LED current limiting demonstrates one of the most common applications of Ohm's Law. LEDs are current-sensitive devices requiring specific current for proper operation, typically 20mA for standard indicator LEDs. However, LEDs have very low forward voltage drop (about 2V for red LEDs, 3-3.5V for white/blue LEDs) and essentially no resistance, so connecting an LED directly to a voltage source results in destructive overcurrent. A current-limiting resistor in series with the LED controls current to safe levels. For a white LED (3V forward drop) powered by 5V USB, the resistor must drop the excess 2V. Using Ohm's Law: R = V / I = 2V / 0.020A = 100Ω. The resistor dissipates P = I²R = (0.020)² × 100 = 0.04W, so a 1/8 watt resistor suffices.
Wire gauge selection for power distribution relies on Ohm's Law to limit voltage drop and prevent overheating. A 12V DC solar installation with a 10A load located 50 feet from the battery bank requires careful wire sizing. Suppose 14 AWG wire is initially considered, with resistance of about 2.5Ω per 1,000 feet. For the 100-foot round trip (50 feet each way), total resistance equals 100ft × 2.5Ω/1000ft = 0.25Ω. Voltage drop equals I × R = 10A × 0.25Ω = 2.5V, representing over 20% loss, completely unacceptable. Upgrading to 10 AWG (1.0Ω per 1,000 feet) reduces drop to 10A × 0.1Ω = 1V (8.3%), better but still problematic. Moving to 8 AWG (0.6Ω per 1,000 feet) yields 10A × 0.06Ω = 0.6V (5%), acceptable for most applications. This demonstrates why low-voltage DC systems require heavier gauge wire than equivalent AC systems.
Motor starting current analysis requires understanding that motors draw much higher current during startup than during running. A 1-horsepower motor operating at 120V draws about 10A running current. Using P = V × I, running power is 120V × 10A = 1,200W. However, starting current may reach 60A (6× running current) for several seconds. The circuit must handle this inrush without excessive voltage drop that prevents motor starting. If the circuit has 0.5Ω total resistance (wire + connections), voltage drop during starting equals 60A × 0.5Ω = 30V, leaving only 90V at the motor, potentially insufficient for starting. This explains why motors require dedicated circuits with appropriately sized conductors, and why lights dim momentarily when large motors start—the starting current causes temporary voltage drop affecting other loads on the same circuit.
Electrical shock occurs when current passes through the human body, with severity depending on current magnitude, path through the body, and duration. The human body has resistance ranging from about 1,000Ω (wet skin, hand-to-hand contact) to 100,000Ω (dry skin, finger contact). Using Ohm's Law, 120V across 1,000Ω body resistance drives 120mA of current, well into the lethal range. Current effects on the human body include: 1mA = barely perceptible, 5mA = pain, 10-20mA = sustained muscular contraction (cannot let go), 30mA = respiratory paralysis, 75-100mA = ventricular fibrillation (usually fatal), 200mA+ = severe burns and cardiac arrest. This is why even modest voltages are dangerous when low-resistance paths exist, such as wet conditions, broken skin, or hand-to-hand contact.
Ground Fault Circuit Interrupters (GFCIs) protect against electrocution by detecting current imbalances as small as 4-6mA between hot and neutral conductors, indicating current leaking through an unintended path (potentially through a person). GFCIs trip within 25 milliseconds when detecting such faults, interrupting current before it can cause ventricular fibrillation. Electrical codes require GFCI protection for outlets in wet locations (bathrooms, kitchens, outdoors, garages, basements) because water dramatically reduces skin resistance, increasing shock hazard. Arc Fault Circuit Interrupters (AFCIs) detect dangerous arcing conditions that can ignite fires, required by modern codes in bedrooms and living areas.
Overcurrent protection using circuit breakers and fuses prevents wiring overheating and fires by interrupting excessive current. Current flowing through wire resistance generates heat according to P = I²R. Notice the squared relationship: doubling current quadruples heat generation. A 20A circuit breaker protects 12 AWG copper wire rated for 20A at 75°C. If a fault allows 40A to flow, heat generation increases by (40/20)² = 4×, potentially melting insulation and igniting surrounding materials within minutes. Circuit breakers and fuses sized according to conductor ampacity ensure protective devices trip before conductors overheat. This is why using higher-rated breakers or bypassing protection devices is extremely dangerous, removing the safety mechanism that prevents wire overheating and fire.
Arc flash hazards in high-power electrical systems can release tremendous energy in milliseconds, causing severe burns, hearing damage, and fatal injuries. Arc flash energy depends on fault current, system voltage, and clearing time. A fault on a 480V three-phase system with 40,000A available fault current (determined by source impedance and conductor sizes) can release over 50,000 joules of energy per millisecond, vaporizing copper and creating a plasma ball expanding at supersonic speeds. Arc flash calculations determine required personal protective equipment (PPE) and safe working distances. This demonstrates why only qualified electricians should work on energized equipment, particularly high-power industrial systems where fault currents can be devastating. Proper procedures include deenergizing circuits, lockout/tagout, voltage testing to verify deenergization, and using appropriate arc-rated PPE when energized work is unavoidable.
Kirchhoff's Voltage Law (KVL) states that the sum of voltages around any closed loop in a circuit equals zero, or equivalently, the sum of voltage rises equals the sum of voltage drops. This law extends Ohm's Law to complex circuits with multiple voltage sources and resistances. For a simple series circuit with a 12V battery and three resistors dropping 3V, 4V, and 5V respectively, KVL confirms: +12V - 3V - 4V - 5V = 0. For circuits with multiple loops, KVL equations for each loop create a system of simultaneous equations that can be solved to find all currents and voltages. This technique, called mesh analysis, forms the foundation of computer circuit simulation programs like SPICE.
Kirchhoff's Current Law (KCL) states that the sum of currents entering a node equals the sum of currents leaving that node, reflecting conservation of charge. At a junction where a 5A current splits into three parallel branches carrying 2A, 1.5A, and 1.5A respectively, KCL confirms: 5A = 2A + 1.5A + 1.5A. KCL applies at every node in a circuit, creating equations that relate branch currents. Nodal analysis uses KCL equations for each node (except the reference node) to solve circuit behavior. Together, KVL and KCL provide the mathematical framework for analyzing any linear circuit, no matter how complex, though practical circuit analysis often combines these laws with Ohm's Law and circuit simplification techniques like series/parallel reduction and Thevenin/Norton equivalents.
Superposition theorem allows analyzing circuits with multiple voltage sources by considering one source at a time while replacing other voltage sources with short circuits (wire) and current sources with open circuits (remove). Calculate the effect of each source independently using Ohm's Law and series/parallel analysis, then sum the results. For example, analyzing a circuit with both a 12V battery and a 5V battery involves calculating currents due to the 12V source alone (with 5V replaced by a wire), then calculating currents due to the 5V source alone (with 12V replaced by a wire), then adding the results algebraically (considering direction). Superposition works because electrical circuits are linear systems where the response to multiple stimuli equals the sum of individual responses.
Thevenin's theorem simplifies complex circuits by replacing everything except the load with an equivalent voltage source (Thevenin voltage) in series with an equivalent resistance (Thevenin resistance). To find Thevenin equivalent: remove the load, calculate open-circuit voltage at the load terminals (Thevenin voltage), then replace all sources with their internal impedances and calculate resistance seen from the load terminals (Thevenin resistance). The resulting simple two-component circuit behaves identically to the original complex circuit from the load's perspective. This technique dramatically simplifies analysis of circuits where the load varies or when investigating load effects. Norton's theorem provides a similar simplification using a current source in parallel with Norton resistance, with simple conversions between Thevenin and Norton equivalents.