Final Velocity CalculatorKnow any three of u, v, a, t, s? Solve the other two.
A complete SUVAT solver for constant acceleration, with the equation it used, every step, and a velocity–time graph.
By Manzoor Ahmad, pharmacist · Updated How do you calculate final velocity?
Use v = u + at when you know the time, or v = √(u² + 2as) when you know the distance. A car moving at 10 m/s that accelerates at 2 m/s² for 5 s reaches v = 10 + 2 × 5 = 20 m/s, covering s = ut + ½at² = 75 m along the way.
The five SUVAT equations
Each equation leaves out one variable. Choose the one that skips the value you neither know nor need.
| Equation | Leaves out | Use it when |
|---|---|---|
| v = u + at | s | you know the time and need the final speed |
| s = ut + ½at² | v | you need distance from starting speed, time and acceleration |
| v² = u² + 2as | t | time is unknown, such as braking distance problems |
| s = ½(u + v)t | a | you know both speeds and the time |
| s = vt − ½at² | u | you know the end state but not the start |
Worked examples
1. Speeding up
u = 10 m/s, a = 2 m/s², t = 5 s. v = 10 + 2 × 5 = 20 m/s; s = 10 × 5 + ½ × 2 × 25 = 75 m. This is the default.
2. Ball thrown straight up
With up as positive, a = −9.81 m/s². If it takes 2.0 s to reach the top (v = 0): u = v − at = 19.62 m/s, and the maximum height is s = vt − ½at² = 19.62 m.
3. Braking that never stops
u = 10 m/s, a = −2 m/s², s = 100 m: v² = 100 − 400 is negative, which means the car stops before 100 m. It actually stops after u² ÷ 2|a| = 25 m.
Final velocity FAQs
With constant acceleration, final velocity is v = u + at, where u is initial velocity, a is acceleration and t is time. If time is unknown, use v² = u² + 2as.
Use v = √(u² + 2as). A car starting at 10 m/s and accelerating at 2 m/s² over 75 m reaches √(100 + 300) = 20 m/s.
They are the five constant-acceleration equations: v = u + at; s = ut + ½at²; v² = u² + 2as; s = ½(u + v)t; and s = vt − ½at². Each leaves out one of the five variables.
S is displacement, U is initial velocity, V is final velocity, A is acceleration and T is time. Knowing any three lets you find the other two.
Pick the equation that contains the three values you know and the one you want, and leaves out the one you neither know nor need. This calculator chooses automatically.
Yes. A negative velocity means the object is moving in the opposite direction to the one you chose as positive, for example a ball that has passed its highest point and is falling back.
Speed is how fast something moves. Velocity is speed with a direction. In one-dimensional problems the sign of velocity shows the direction.
You need a third value. If the object starts from rest, v = 2s ÷ t. If it moves at constant speed, v = s ÷ t.
Yes. Use a = 9.81 m/s² (or −9.81 if up is positive). For a dedicated tool with drop height and impact speed, use the free fall calculator.
Equations with squares, like v² = u² + 2as, have a positive and a negative root. The calculator reports the physically likely one and notes when the other is possible, such as an object passing the same point twice.
Any consistent SI set works best: m/s, m/s², s and m. The calculator converts km/h, mph and feet automatically.
The SUVAT equations only apply to constant acceleration. For changing acceleration you need calculus or numerical methods, and these equations give at best an average.
Sources
- OpenStax University Physics Volume 1, Section 3.4: Motion with Constant Acceleration
- OpenStax University Physics Volume 1, Section 3.5: Free Fall
- NIST CODATA: Standard acceleration of gravity
- NIST SP 811: Guide for the Use of the International System of Units
- NASA Glenn Research Center: Motion equations
This final velocity calculator assumes constant acceleration in one dimension and no air resistance. Choose one direction as positive and keep signs consistent.