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Formula
v = d ÷ t, v = v₀ + a × t
- v
- velocity (average velocity in the first form, final velocity in the second), in m/s
- d
- distance traveled, in meters (m)
- t
- time taken, in seconds (s)
- v₀
- initial velocity, in m/s
- a
- constant acceleration, in m/s²
What velocity is
Velocity describes how fast something moves and in which direction. In one dimension, the direction is just a sign: positive one way, negative the other. In everyday use, “velocity” and “speed” are often used interchangeably, and for straight-line motion in one direction they give the same number.
Two equations cover most velocity questions:
- Average velocity: v = d ÷ t. The distance traveled divided by the time it took.
- Final velocity under constant acceleration: v = v₀ + at. The starting velocity plus the speed gained (or lost) at a steady rate.
This velocity calculator has a tab for each, plus two more that rearrange v = d ÷ t to find a distance or a travel time.
How to use the velocity calculator
- Pick a tab. v = d ÷ t gives average velocity. v = v₀ + at gives final velocity. Distance and Time solve the other parts of the speed–distance–time triangle.
- Enter your values with their units. Distance can be in meters, kilometers, feet, miles or nautical miles. Time can be in seconds, minutes or hours. Velocity can be in m/s, km/h, mph, ft/s or knots, and acceleration in m/s², ft/s² or g.
- Choose the unit for the answer. Every other unit appears below it.
- Extra rows depend on the tab. For walking and running speeds you get your pace per kilometer and per mile. The v₀ + at tab also gives the distance covered and the average velocity.
How to calculate velocity by hand
Average velocity. A coach covers 150 km in 2 hours. v = 150 km ÷ 2 h = 75 km/h. In SI units: 150,000 m ÷ 7,200 s ≈ 20.83 m/s.
Final velocity. A bike moving at 4 m/s accelerates at 1.5 m/s² for 6 s. v = 4 + 1.5 × 6 = 4 + 9 = 13 m/s.
Distance and time. Rearranging v = d ÷ t gives d = v × t and t = d ÷ v. At 60 mph, 240 miles takes 240 ÷ 60 = 4 hours. In 45 minutes at 60 mph, you cover 60 × 0.75 = 45 miles.
Always make the units agree before dividing. Kilometers with hours gives km/h. Meters with seconds gives m/s. Kilometers with minutes gives km/min, which is rarely what you want.
Velocity unit conversions
| m/s | km/h | mph | ft/s |
|---|---|---|---|
| 1 | 3.6 | 2.237 | 3.281 |
| 5 | 18 | 11.18 | 16.4 |
| 10 | 36 | 22.37 | 32.81 |
| 20 | 72 | 44.74 | 65.62 |
| 30 | 108 | 67.11 | 98.43 |
| 50 | 180 | 111.8 | 164 |
| 100 | 360 | 223.7 | 328.1 |
For any other value, use the speed converter.
Average speed vs. average of speeds
Suppose you drive 60 miles at 30 mph, then 60 miles back at 60 mph. The average of the two speeds is 45 mph, but that is wrong. The first leg takes 2 hours and the second takes 1 hour, so the true average speed is 120 miles ÷ 3 hours = 40 mph. You spend more time at the slower speed, so it counts for more. The v = d ÷ t tab gets this right if you enter the total distance and total time.
Real-life uses
Travel planning
Divide the distance by your expected average speed to estimate a travel time, or use a past trip’s distance and time to find your real average speed, stops included.
Running and cycling
Runners usually think in pace (minutes per mile) rather than speed. The calculator shows both. The pace calculator goes further, with splits and race-time targets.
Velocity of a falling object
Free-fall problems use v = v₀ + at with a = g (9.80665 m/s², or 32.17 ft/s²). Ignoring air resistance, an object dropped from rest is moving at 9.80665 × 2 ≈ 19.6 m/s after 2 seconds. Choose g as the acceleration unit and enter 1 to do this directly. Braking problems use the same formula with a negative acceleration. To find the acceleration from two speeds instead, use the acceleration calculator. For the energy of the moving object, use the kinetic energy calculator.
Common mistakes
- Averaging speeds instead of dividing total distance by total time.
- Mixing minutes and hours. 45 minutes is 0.75 h, not 0.45 h.
- Forgetting the sign of acceleration. Braking is negative, so v = v₀ + at decreases.
- Applying v = v₀ + at when acceleration changes. The formula needs constant acceleration.
- Confusing velocity with distance per lap. Average velocity uses displacement, so a full lap has zero average velocity even though the average speed is not zero.
Glossary
- Displacement: the straight-line change in position, with direction.
- Average velocity: displacement divided by elapsed time.
- Instantaneous velocity: the velocity at one moment, what a speedometer shows.
- Initial velocity (v₀): the velocity at the start of the time interval.
- Pace: time per unit distance, the reciprocal of speed.
Worked examples
Average speed of a road trip
You drive 186 miles in 3 hours including stops.
Inputs (v = d ÷ t): Distance = 186; Distance unit = Miles; Time = 3; Time unit = Hours; Show velocity in = Miles per hour (mph)
Convert to SI units: 186 mi = 299,338 m; 3 h = 10,800 s v = d ÷ t = 299,338 m ÷ 10,800 s = 27.7165 m/s 27.7165 m/s = 62 mph
Answer: 186 mi in 3 h is an average velocity of 62 mph.
A sprinter’s average velocity
A runner covers 200 m in 25 seconds.
Inputs (v = d ÷ t): Distance = 200; Distance unit = Meters; Time = 25; Time unit = Seconds; Show velocity in = Meters per second (m/s)
v = d ÷ t = 200 m ÷ 25 s = 8 m/s
Answer: 200 m in 25 s is an average velocity of 8 m/s.
Final velocity of a falling object
An object dropped from rest falls for 3 seconds, ignoring air resistance (a = g = 9.80665 m/s²).
Inputs (v = v₀ + at): Initial velocity (v₀) = 0; Initial velocity (v₀) unit = Meters per second; Acceleration (a) = 9.80665; Acceleration (a) unit = Meters per second squared; Time = 3; Time unit = Seconds; Show velocity in = Meters per second (m/s)
v = v₀ + a × t = 0 m/s + (9.80665 m/s²) × 3 s = 29.42 m/s
Answer: Starting at 0 m/s and accelerating at 9.80665 m/s² for 3 s, the final velocity is 29.42 m/s.
Edge case: braking past zero
A cart moving at 12 m/s decelerates at 4 m/s² for 5 s. It stops after 3 s, so the formula gives a negative (reversed) velocity.
Inputs (v = v₀ + at): Initial velocity (v₀) = 12; Initial velocity (v₀) unit = Meters per second; Acceleration (a) = -4; Acceleration (a) unit = Meters per second squared; Time = 5; Time unit = Seconds; Show velocity in = Meters per second (m/s)
v = v₀ + a × t = 12 m/s + (−4 m/s²) × 5 s = −8 m/s
Answer: Starting at 12 m/s and accelerating at −4 m/s² for 5 s, the final velocity is −8 m/s.
Travel time at a steady speed
How long a marathon (42.195 km) takes at a steady 12 km/h.
Inputs (Time): Distance = 42.195; Distance unit = Kilometers; Velocity = 12; Velocity unit = Kilometers per hour; Show time in = Hours (h)
Convert to SI units: 42.195 km = 42,195 m; 12 km/h = 3.33333 m/s t = d ÷ v = 42,195 m ÷ 3.33333 m/s = 12,658.5 s 12,658.5 s = 3.51625 h
Answer: 42.195 km at 12 km/h takes 3.51625 h (3:30:59).
Assumptions and limitations
- v = d ÷ t gives the average velocity over the whole trip, including any stops or slow sections. It treats distance as displacement along a straight line.
- v = v₀ + at assumes constant acceleration over the time entered. A negative acceleration (deceleration) is allowed. A negative result means the object has reversed direction.
- The distance and time modes rearrange v = d ÷ t (d = v × t and t = d ÷ v) and assume a steady average speed.
- Units are converted exactly. 1 mph = 0.44704 m/s, 1 km/h = 1/3.6 m/s, 1 knot = 1,852 m per hour, and 1 g = 9.80665 m/s².
- Results are shown to 6 significant figures. Travel times are also shown as h:mm:ss, rounded to the nearest second.
Frequently asked questions
What is the formula for velocity?
Average velocity is displacement divided by time, v = d ÷ t. Driving 150 km in 2 hours is an average of 75 km/h, or about 20.83 m/s.
How do I calculate final velocity?
With constant acceleration, add the acceleration times the time to the starting velocity, v = v₀ + at. Starting at 4 m/s and accelerating at 1.5 m/s² for 6 s gives 4 + 9 = 13 m/s.
What is the difference between speed and velocity?
Speed is how fast something moves. Velocity is speed in a particular direction. Running one lap of a 400 m track in 80 s is an average speed of 5 m/s. Because you finish where you started, your average velocity is zero.
How do I calculate average speed for a trip with stops?
Divide the total distance by the total elapsed time, stops included. Do not average the speeds of each leg, because you spend more time on the slower legs.
How do I convert m/s to km/h or mph?
Multiply m/s by 3.6 to get km/h, or by about 2.237 to get mph. 10 m/s is 36 km/h or 22.37 mph. The calculator shows every unit below the answer.
How do I find time from distance and speed?
Divide the distance by the speed, t = d ÷ v. 240 miles at 60 mph takes 4 hours. Use the Time tab to get the answer in seconds, minutes, hours or h:mm:ss.
Sources
- University Physics Volume 1, 3.1 Position, Displacement, and Average Velocity — OpenStax (Rice University). Checked October 12, 2026.
- University Physics Volume 1, 3.4 Motion with Constant Acceleration — OpenStax (Rice University). Checked October 12, 2026.
- NIST Guide to the SI, Appendix B.9: Factors for units listed by kind of quantity — National Institute of Standards and Technology (NIST). Checked October 12, 2026.