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
How do I use SUVAT calculator find missing values?
SUVAT problems use five quantities: s (displacement), u (initial velocity), v (final velocity), a (acceleration), t (time). Five equations relate them, each missing one variable. Provide any three knowns, and the calculator picks the right equation to solve for the unknowns. The equations: v = u + at; s = ut + ½at²; v² = u² + 2as; s = ½(u + v)t; s = vt − ½at². Match equation to data: if t isn't given, use v² = u² + 2as. If a isn't given, use s = ½(u + v)t. With practice, the choice becomes automatic.
Which SUVAT equation to use?
Pick by what's missing. If you don't have time, use v² = u² + 2as. If you don't have a (acceleration), use s = ½(u + v)t. If you don't have v (final velocity), use s = ut + ½at². If you don't have s (displacement), use v = u + at. If you don't have u, use s = vt − ½at². Five equations cover all combinations. Always list what you know and what you want; the right equation falls out almost automatically. The calculator does this matching for you, but doing it by hand cements the underlying logic.
How to calculate final velocity with acceleration and time?
Use v = u + at: final velocity equals initial velocity plus acceleration times time. If a car starts at 5 m/s and accelerates at 2 m/s² for 6 seconds, then v = 5 + 12 = 17 m/s. The formula assumes constant acceleration — if a changes, you need calculus or split the motion into segments. Negative acceleration (deceleration) just goes in with its sign, so a car braking at −3 m/s² from 20 m/s for 4 seconds gives v = 20 − 12 = 8 m/s. The simplest of the SUVAT equations and probably the most often used.
How to find displacement using SUVAT?
Three displacement equations: s = ut + ½at² (when you know u, a, t); s = vt − ½at² (when you know v, a, t); s = ½(u + v)t (when you know u, v, t). Pick whichever matches your data. So a 3 m/s start, 2 m/s² acceleration, over 5 seconds gives s = 15 + 25 = 40 m. The third equation uses the average velocity ½(u + v), then multiplies by time. All three give the same answer when used correctly. Always check signs carefully — directions matter, and a wrong sign on acceleration trips up many problems.
How do I use initial velocity calculator SUVAT?
Solve for u using whichever SUVAT equation has it. From v = u + at, u = v − at. From s = ut + ½at², u = (s − ½at²)/t. From v² = u² + 2as, u = √(v² − 2as). Pick the form that matches your knowns. So if a ball reaches 0 m/s after 4 s of −9.8 m/s² deceleration (gravity), then u = 0 − (−9.8)(4) = 39.2 m/s — that's how fast you'd need to throw it up to reach that height. Calculators run the algebra, but understanding which equation you've reversed keeps you honest.
How do I use acceleration from velocity and distance calculator?
When time isn't given, use v² = u² + 2as and solve for a: a = (v² − u²)/(2s). So if a vehicle goes from 10 m/s to 30 m/s over 200 m, then a = (900 − 100)/400 = 2 m/s². This is the go-to equation when problems don't mention time but give you starting and ending speeds plus the distance covered. Often easier than deriving time first and then using v = u + at. The calculator picks this equation automatically when t isn't supplied. Watch out for negative results — they mean deceleration.
How do I use SUVAT equations with no time?
v² = u² + 2as is the time-free equation. Useful when problems specify start velocity, end velocity, and distance, but skip time. Rearrange to get any of the three: v = √(u² + 2as), u = √(v² − 2as), s = (v² − u²)/(2a), a = (v² − u²)/(2s). For free fall from rest over 80 m, v² = 0 + 2 × 9.81 × 80 = 1570, so v ≈ 39.6 m/s. This is essentially energy conservation in disguise — multiply both sides by ½m and you get the work-energy theorem. Same physics, different algebra.
Sources and References
What this calculator does
SUVAT Equations Calculator turns the visible inputs on the page into a specific result and keeps the calculation context close to the form. The added notes identify what the output means, which assumptions matter, and when the result should be checked against source data or official guidance.