SUVAT Calculator
Tell it which three of s, u, v, a and t you know and it solves the other two, names the equation and shows every step.
📏 What is a SUVAT Calculator?
A SUVAT calculator solves problems about motion in a straight line with constant acceleration. SUVAT is the mnemonic for the five quantities involved: s for displacement, u for initial velocity, v for final velocity, a for acceleration and t for time. The key fact is that any three of them determine the other two, so a typical exam question gives you three and asks for one or both of the rest. The five equations of motion link them, and each equation leaves out exactly one variable, which is why picking the right one is the real skill.
The idea is used everywhere speed changes steadily: a car braking to a stop, a sprinter leaving the blocks, a stone dropped from a bridge, a ball thrown upward, a train pulling out of a station or a lift moving between floors. School and university mechanics courses use SUVAT first because it needs only algebra, and it also underpins projectile motion, where the horizontal and vertical parts are each solved as separate constant acceleration problems.
This tool is built around the way you actually solve a question on paper. Instead of leaving boxes blank, you tell it which three quantities you know. It then shows only those inputs, solves the other two, names the equation it used for each, and prints the substitution line by line so you can compare it with your own working. If the data allow two answers, such as a ball passing the same height going up and coming down, it lists both and plots both. It is a different tool from the general kinematic equations calculator, which fills in blanks without showing which relationship it chose.
Remember the limits. SUVAT needs constant acceleration, so it does not apply to a falling object with strong air drag, a rocket burning fuel or a car whose engine force varies. For drag use the terminal velocity calculator, and for two dimensional launches use the projectile motion calculator. Always choose a positive direction first and keep the signs of s, u, v and a consistent with it.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Stone Dropped for 4 Seconds
Dropped from rest (u = 0) with a = 9.8 m/s² downward, t = 4 s
Example 2 — Car Braking to a Stop
A car at 30 m/s (108 km/h) brakes at 8 m/s² until it stops
Example 3 — Ball Thrown Upward Passes 15 m Twice
Thrown up at 20 m/s with a = −9.8 m/s²; when is it 15 m above the hand?
Example 4 — Sprinter Reaches 10 m/s in 20 m
From rest (u = 0) to v = 10 m/s over s = 20 m
Example 5 — Overtaking Car Covers 200 m in 10 s
A car moving at 15 m/s accelerates steadily and covers 200 m in 10 s
Example 6 — Train Slowing Before a Station
A train ends at v = 25 m/s after decelerating at 0.5 m/s² for 20 s; find its speed 20 s earlier and the distance
❓ Frequently Asked Questions
🔗 Related Calculators
What does SUVAT stand for?
SUVAT stands for the five quantities in constant acceleration problems: s is displacement, u is initial velocity, v is final velocity, a is acceleration and t is time. Any three of them fix the other two.
What are the SUVAT equations?
There are five: v = u + at, s = ut + 0.5at^2, v^2 = u^2 + 2as, s = 0.5(u + v)t and s = vt - 0.5at^2. Each one leaves out exactly one of the five variables, which is how you choose between them.
How do I choose the right SUVAT equation?
Find the variable that is neither given nor asked for and pick the equation without it. If time is missing use v^2 = u^2 + 2as. If displacement is missing use v = u + at. If acceleration is missing use s = 0.5(u + v)t.
Why does the SUVAT calculator sometimes give two answers?
When you know s, u and a, or s, v and a, the unknown velocity comes from a square root, so there are two roots. A ball launched upward at 20 m/s passes a 15 m height at 0.99 s on the way up and 3.09 s on the way down.
Can SUVAT be used when acceleration changes?
No. The equations assume constant acceleration in a straight line. For drag, rocket thrust or any acceleration that varies with time or speed you need calculus or numerical integration.
How do I handle negative values in SUVAT?
Negative simply means opposite to your chosen positive direction. A car braking from 30 m/s to rest has u = 30, v = 0 and a = -8 with forward as positive, giving a stopping distance of 56.25 m.
What value of g should I use in SUVAT problems?
Use 9.8 or 9.81 m/s2 for most school problems, with the sign matching your convention. The standard value is 9.80665 m/s2. Enter a = 9.8 for downward positive free fall, or a = -9.8 for upward positive.
How do I find displacement without knowing time?
Use v^2 = u^2 + 2as rearranged to s = (v^2 - u^2) / (2a). Select u, v and a as the known quantities and the calculator also returns the time from v = u + at.
What if my answer for time is negative?
A negative time means the inputs describe a situation that would have happened before the start, so they are inconsistent for forward motion. The calculator reports this instead of giving a meaningless number.
How is this different from the kinematic equations calculator?
This page lets you declare exactly which three quantities you know, shows the equation used for each unknown, writes out the substitution step by step, lists both roots when there are two, and draws the velocity-time graph.
Does SUVAT work for vertical motion?
Yes, as long as air resistance is negligible. Treat gravity as a constant acceleration of 9.8 m/s2 downward, choose up or down as positive and keep the signs consistent for s, u, v and a.