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Velocity Calculator

Find average velocity from displacement and time, solve for the displacement or time instead, or get final velocity from v = u + at.

Level: Grades 8–9

Printable worksheet

Velocity Calculator

Know the answer you need? Pick an input to work backward.

Inputs
Solve for

Straight-line change in position. Negative means it ended up behind where it started.

Result

Average velocity

80 km/h

Average velocity is 80 km/h.

In meters per second
22.2222 m/s
In miles per hour
49.7097 mph
In knots
43.1965 kn
In feet per second
72.9076 ft/s

See the step-by-step solution ↓

Step-by-step solution

  1. Change displacement to m, the standard unit the formula uses (1 km = 1,000 m)

    120 km×1,000=120,000 m

  2. Change time to s, the standard unit the formula uses (1 h = 3,600 s)

    1.5 h×3,600=5,400 s

  3. Divide how far it moved (the displacement) by the time it took, to get the average velocity

    120,0005,400=22.222222 m/s

  4. Change the answer to km/h, the unit you picked: divide by 0.277777777778

    22.2222220.277777777778=80 km/h

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

What this calculator does

Find out how fast something is moving, and in which direction. That's what velocity means: speed plus direction. Average velocity is the displacement divided by the time taken. Displacement is the straight-line change in position, from start to finish. Because it has a direction, velocity can be negative. For example, a car that reverses 30 m in 10 s has a velocity of −3 m/s along the road.

This calculator finds whichever of the three you're missing: velocity, displacement or time. It works in metric or US units. A fourth mode answers another common motion question. Say something starts at velocity u and speeds up steadily, at an acceleration a, for a time t. How fast is it going at the end? That uses v = u + at. The calculator also tells you how far it traveled on the way.

Where it's used

Why this math matters outside the classroom:

  • Road trips. A driver covering 150 km in 2 hours averages 75 km/h, even with stops and speed changes along the way.
  • Laps on a track. A runner who finishes a 400 m lap ends where they started, so their average velocity for the lap is zero.
  • Speeding up. A cyclist at 4 m/s speeding up at 0.5 m/s² for 10 s reaches 4 + 0.5 × 10 = 9 m/s.
  • Arrival times. Ship navigators estimate arrival times from a vessel's speed in knots and the distance still to go.

Grade level and standards: Grades 8–9; Common Core State Standards for Mathematics HSA.CED.A.4. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

  1. Choose what to solve for: average velocity, displacement, time, or final velocity with v = u + at.
  2. Enter the known values and pick a unit beside each one. Use negative numbers for motion in the opposite direction.
  3. Choose the unit for the answer. You'll also see the result in the other speed, length or time units.
  4. Read the working below the result. It shows each unit conversion and the formula with your numbers in it.

What the inputs mean

Displacement (Δx)
Displacement isn't the same as distance traveled. A runner who finishes one full lap of a 400 m track has run 400 m. But they ended where they started, so their displacement is zero, and so is their average velocity for the lap.
Average velocity (v)
Use the average velocity over the whole trip, not the top speed or a reading at one moment.
Acceleration (a)
v = u + at only works while the acceleration stays the same. A negative value with a positive starting velocity (u) means the object is slowing down.
Time (t)
How long the steady acceleration lasts. If you enter zero, you just get back the starting velocity.

Formula and method

v̄ = Δx ÷ t
Δx = v̄ × t
t = Δx ÷ v̄
v = u + a × t
s = u × t + ½ × a × t²

In the formulas, v̄ is the average velocity, Δx is the displacement (the change in position) and t is the time. The first three lines are one idea, rearranged to solve for each of the three. The calculator first converts every input to meters, seconds and meters per second. Then it does the math and converts the answer to the unit you chose.

The last two lines are for steady (constant) acceleration. Here u is the starting velocity, a is the acceleration, v is the final velocity and s is the distance moved. With acceleration a lasting for time t, the velocity changes by a × t. The distance moved in that time is u × t + ½ × a × t². With steady acceleration, the average velocity is exactly halfway between u and v.

Worked example

A train covers 120 km of straight track in 1.5 hours. What is its average velocity?

  1. Convert the displacement: 120 km × 1,000 = 120,000 m.
  2. Convert the time: 1.5 h × 3,600 = 5,400 s.
  3. Average velocity = 120,000 ÷ 5,400 = 22.222222 m/s.
  4. Convert to km/h: 22.222222 ÷ 0.277778 = 80 km/h (about 49.71 mph).

Result: The train averages 80 km/h. In the v = u + at mode, picture a cyclist starting at 5 m/s and speeding up at 2.5 m/s² for 8 s. They reach 25 m/s (90 km/h) and cover 120 m.

Understanding the result

An average velocity says nothing about what happened along the way. The train above may have stopped at a station, then run faster than 80 km/h to make up the time. Only the start, the end and the time taken matter.

A negative result means the overall movement was in the direction you treat as negative. The size of the number equals the average speed only if the motion was in a straight line, with no turning back.

Assumptions and limitations

  • The motion is along one straight line, and one direction is chosen as positive.
  • For v = u + at, the acceleration stays the same for the whole time.
  • Speeds are far below the speed of light, so everyday (classical) physics applies.
  • Average velocity uses the overall change in position. For a winding route or a round trip, use the total distance and an average speed instead.
  • Real vehicles rarely speed up at a perfectly steady rate, so v = u + at gives an idealized estimate.
  • Motion in two or three dimensions needs velocity components or vectors. This calculator works along a single line.

Frequently asked questions

What is the difference between velocity and speed?

Speed is how fast something moves. Velocity is speed with a direction. Average speed divides the total distance by the time. Average velocity divides the overall change in position by the time. So a round trip has a positive average speed but zero average velocity.

Can velocity be negative?

Yes. A negative velocity means motion in the direction you've chosen as negative, such as reversing, or falling when up is positive. Time can't be negative, though. So when solving for time, the calculator asks for a displacement and velocity with matching signs.

When can I use v = u + at?

Use it whenever the acceleration stays the same the whole time. Examples are a ball dropped near the ground (ignoring air resistance), a car pulling away at a steady rate, or a vehicle braking evenly. If the acceleration changes, split the motion into pieces where it's roughly steady.

How do I convert between km/h and m/s?

Divide km/h by 3.6 to get m/s, or multiply m/s by 3.6 to get km/h. One mile per hour is exactly 0.44704 m/s.

How this calculator is checked

Method: Definition of average velocity (Δx ÷ t) and the constant-acceleration equations v = u + at and s = ut + ½at². The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

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