Velocity Calculator
Find velocity from distance and time, acceleration from a change in speed, or any two unknowns with the SUVAT equations of motion. Units convert automatically and every step is shown, all privately in your browser.
v = d / t
a = (v₁ − v₀) / t
v = u + at · s = ut + ½at² · v² = u² + 2as
Enter any three of the five values and leave the other two blank. Negative values mean the opposite direction (e.g. braking).
Step-by-step solution
How to use the Velocity Calculator
- Pick a mode: Velocity for d/t, Acceleration for a change of speed, or Kinematics (SUVAT) for constant acceleration problems.
- Choose what to solve for with the Solve for buttons (in SUVAT, simply leave the two unknowns blank).
- Enter the known values and choose units such as km/h, mph, m/s², g, seconds or hours.
- Read the answer in the highlighted field; change its unit to convert it instantly.
- Check the steps and press Copy result to paste the answer with its inputs.
Velocity, acceleration and the SUVAT equations
Velocity is the rate of change of position: v = d / t. Rearranged, distance is d = v × t and time is t = d / v. Acceleration is the rate of change of velocity: a = (v₁ − v₀) / t, measured in metres per second squared (m/s²).
When the acceleration is constant, five quantities describe the motion: displacement s, initial velocity u, final velocity v, acceleration a and time t. Each of the five SUVAT equations leaves out one of them, so any three known values are enough:
| Equation | Missing variable |
|---|---|
| v = u + at | s |
| s = ut + ½at² | v |
| s = vt − ½at² | u |
| s = ½(u + v)t | a |
| v² = u² + 2as | t |
Worked examples
- Car acceleration: 0 to 100 km/h in 8 s. 100 km/h = 27.78 m/s, so a = 27.78 / 8 = 3.47 m/s² (0.354 g), and the car covers ½ × 27.78 × 8 = 111 m.
- Braking distance: from 100 km/h (27.78 m/s) at −7 m/s². Using v² = u² + 2as with v = 0 gives s = 27.78² / (2 × 7) = 55.1 m, and t = 27.78 / 7 = 3.97 s (braking only, without reaction time).
- Dropped object: u = 0, a = 9.81 m/s², t = 3 s gives v = 29.4 m/s and s = ½ × 9.81 × 3² = 44.1 m, ignoring air resistance.
- Ball thrown upward: u = 20 m/s, a = −9.81 m/s², s = 10 m. It is 10 m high at t = 0.58 s on the way up and again at t = 3.49 s on the way down.
Common speed and acceleration conversions
| Unit | In SI |
|---|---|
| 1 km/h | 0.277778 m/s |
| 1 mph | 0.44704 m/s (1.609344 km/h) |
| 1 knot | 0.514444 m/s (1.852 km/h) |
| 1 ft/s | 0.3048 m/s |
| 1 g (standard gravity) | 9.80665 m/s² |
| 1 ft/s² | 0.3048 m/s² |
For everyday trip planning with arrival times, use the speed distance time calculator; for runners, the running pace calculator converts speed to pace per kilometre or mile.
Frequently asked questions
How do you calculate velocity?
Average velocity is displacement divided by time: v = d / t. Driving 100 km in 1 hour 15 minutes (1.25 h) gives 100 / 1.25 = 80 km/h, which is 22.2 m/s or 49.7 mph.
How do you calculate acceleration?
Acceleration is the change in velocity divided by the time it takes: a = (v₁ − v₀) / t. A car going from 0 to 100 km/h (27.78 m/s) in 8 seconds accelerates at 27.78 / 8 = 3.47 m/s², about 0.35 g.
What is the difference between speed and velocity?
Speed is how fast something moves; velocity is speed in a given direction, so it can be negative. In this calculator a negative velocity or acceleration means the opposite direction, which is how you model braking or an object thrown upward.
What are the SUVAT equations?
For constant acceleration: v = u + at, s = ut + ½at², s = vt − ½at², s = (u + v)t / 2 and v² = u² + 2as, where s is displacement, u initial velocity, v final velocity, a acceleration and t time. Knowing any three lets you find the other two.
Why does the SUVAT solver sometimes show two solutions?
When you give s, u and a (or s, v and a), the velocity comes from a square root, so it can be positive or negative. Physically, an object thrown upward passes a given height twice: once rising and once falling. Both valid times are listed.
How do I convert acceleration to g-force?
Divide by standard gravity, 9.80665 m/s². For example 3.47 m/s² ÷ 9.80665 = 0.354 g. You can also pick g as the acceleration unit and the calculator converts automatically.
Do these formulas work if acceleration changes?
v = d/t always gives the average velocity. The acceleration and SUVAT results assume constant (uniform) acceleration; for changing acceleration they give the average acceleration over the interval.