Velocity Calculator

How to Calculate Velocity

Velocity describes how fast an object moves and in which direction. In everyday problems where an object travels in a straight line, average velocity equals the distance (displacement) divided by the time taken. When an object speeds up or slows down at a constant rate, the kinematic equation v = u + at gives its velocity after a given time.

Velocity Formulas

v = d ÷ t   |   d = v × t   |   t = d ÷ v
v = u + a·t

• v = velocity (final velocity in v = u + at)
• d = distance or displacement
• t = time
• u = initial velocity
• a = constant acceleration

Worked Examples

Average velocity: a car travels 100 km in 2 hours. v = 100 km ÷ 2 h = 50 km/h, which is 13.89 m/s or about 31.07 mph.

Final velocity: a ball dropped from rest (u = 0) accelerates at 9.8 m/s² for 3 seconds. v = 0 + 9.8 × 3 = 29.4 m/s (ignoring air resistance).

Unit Conversions

• 1 m/s = 3.6 km/h
• 1 mph = 1.609344 km/h = 0.44704 m/s
• 1 ft/s = 0.3048 m/s

Velocity vs. Speed

Speed is a scalar: it only has a size. Velocity is a vector: it has a size and a direction. For motion along a straight line in one direction the numbers are the same, which is why this calculator treats distance and displacement interchangeably. If an object changes direction, average velocity uses net displacement, so it can be smaller than average speed.

Frequently Asked Questions

What is the formula for velocity?

Average velocity is displacement divided by time, v = d / t. If acceleration is constant, final velocity is v = u + at, where u is the initial velocity, a is acceleration, and t is time.

How do I convert m/s to km/h?

Multiply by 3.6. For example, 10 m/s × 3.6 = 36 km/h. To go from km/h to m/s, divide by 3.6.

What is the difference between speed and velocity?

Speed only tells you how fast something moves. Velocity also includes direction, so it can be negative or change when the direction changes even if the speed stays the same.

Can velocity be negative?

Yes. A negative velocity means motion in the opposite direction to the one you chose as positive. In the v = u + at mode you can enter negative initial velocity or acceleration.

How do I find time from distance and velocity?

Divide the distance by the velocity: t = d / v. For example, 150 miles at 60 mph takes 2.5 hours.

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