SUVAT Equations Calculator
Enter any 3 of u, v, a, t, s and get the remaining two — with the formula used and the full step-by-step working.
Leave the variables you don't know blank. Fill in any three.
The five SUVAT equations
2. s = u·t + ½·a·t²
3. v² = u² + 2·a·s
4. s = ½·(u + v)·t
5. s = v·t − ½·a·t²
How to use
- Type the three known values into their fields. Use negative numbers for quantities pointing against your chosen positive direction.
- Leave the two unknowns blank.
- Click Solve. The tool picks the correct SUVAT equation, substitutes numbers and shows the working.
Physics behind SUVAT
SUVAT equations describe motion under constant acceleration. They are derived from the definitions of velocity and acceleration together with the fact that, for a constant acceleration, the average velocity during the interval equals (u + v)/2. Together the five equations let you solve any kinematics problem as long as acceleration is uniform — for example a falling stone (a = g), a car braking at constant deceleration, or a ball rolling down a ramp.
If acceleration is changing (air resistance, variable thrust, simple harmonic motion), SUVAT no longer applies and you need calculus, differential equations or numerical methods.
Worked example
A car accelerates from rest at 2 m/s² for 5 s. Find v and s.
Known: u = 0, a = 2, t = 5 v = u + at = 0 + 2·5 = 10 m/s s = ut + ½at² = 0 + ½·2·25 = 25 m
Common mistakes
- Using SUVAT when acceleration varies.
- Getting signs wrong. Pick a positive direction and stick to it.
- Mixing up u and v. u is the initial velocity, v is the final.
Related tools
FAQs
What does SUVAT stand for?
S = displacement, U = initial velocity, V = final velocity, A = acceleration, T = time.
When do SUVAT equations apply?
Only when acceleration is constant. For changing acceleration, use calculus or numerical methods.
How many values do I need to enter?
Any three of the five variables.
Can acceleration be negative?
Yes. A negative value just means deceleration relative to your chosen positive direction.