SUVAT Calculator (Kinematics)
Enter any three of the five kinematic variables, displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t), and the calculator solves for the other two. It works through all five SUVAT equations automatically, shows step-by-step working, and lets you switch between metric and imperial units. Gravity presets for Earth, the Moon and Mars are included for projectile and free-fall problems.
Formula
Worked example
A car starts from rest (u = 0) and accelerates at 5 m/s^2 for 10 s. Using v = u + at: v = 0 + 5 x 10 = 50 m/s. Using s = ut + (1/2)at^2: s = 0 + 0.5 x 5 x 100 = 250 m. All five equations are consistent: v^2 = 2 x 5 x 250 = 2500, so v = 50 m/s.
What does SUVAT mean?
SUVAT is an acronym for the five kinematic variables used in constant-acceleration problems: s (displacement), u (initial velocity), v (final velocity), a (acceleration), and t (time). The five SUVAT equations each link four of the five variables, so if you know any three you can always find the other two. They apply strictly to motion in a straight line with a constant (uniform) acceleration. Common real-world scenarios include free fall under gravity, a car braking uniformly, or a ball thrown vertically upward.
How to use this calculator
Type values into any three of the five fields and leave the other two blank. The calculator tries every SUVAT equation in sequence, fills in each unknown as soon as enough information is available, and repeats until all five variables are determined. If a solution exists it is displayed instantly with full step-by-step working. Use the unit selector to switch between metres/seconds and feet/seconds. The gravity preset fills in the acceleration field automatically for free-fall problems on Earth, the Moon or Mars.
The five SUVAT equations explained
v = u + at links velocity and time but ignores displacement - useful when you know acceleration and duration but not distance. s = (u + v)/2 x t is the average-velocity form - distance equals the mean speed multiplied by time, with no need to know acceleration explicitly. v^2 = u^2 + 2as is the time-independent equation - it lets you find final speed after travelling a known distance, without knowing how long it took. s = ut + (1/2)at^2 is the most-used form in free-fall: displacement given initial speed, acceleration and time. s = vt - (1/2)at^2 is the mirror image - it uses final velocity instead of initial velocity, handy when you know where the object ended up but not where it started in terms of speed.
Limitations: when SUVAT does not apply
SUVAT only holds for straight-line motion with perfectly constant acceleration. It does not apply to projectile motion in two dimensions (use the projectile motion calculator), circular motion (centripetal acceleration continuously changes direction), or any situation where acceleration itself varies over time, such as air-resistance drag or a rocket burning fuel. For those cases you need calculus-based kinematics or numerical integration. Within its limits, SUVAT covers an enormous range of practical problems in A-level physics and engineering mechanics.
The five SUVAT equations
| Equation | Missing variable | Use when... |
|---|---|---|
| v = u + at | s | displacement not needed |
| s = (u + v)/2 x t | a | acceleration not needed |
| v^2 = u^2 + 2as | t | time not needed |
| s = ut + (1/2)at^2 | v | final velocity not needed |
| s = vt - (1/2)at^2 | u | initial velocity not needed |
Each equation omits one of the five variables. Identify which variable is unknown and use the equation that does not contain it.
Frequently asked questions
Can I leave more than two fields blank?
No. The five SUVAT equations each contain four variables, so you need at least three known values to have a unique solution. With only two known values there are infinitely many consistent motions. Provide a third value and the calculator will solve the remaining two.
What if I get no solution or an error message?
A set of three values has no real solution when they describe a physically impossible scenario, for example a positive displacement with a large negative acceleration and a long time that would require the object to travel backward further than it went forward. Double-check your numbers and signs. Velocity and acceleration can be negative (opposite direction), but time must be non-negative.
How do I handle free fall with SUVAT?
Set u = 0 (dropped from rest) or the launch speed, set a = 9.807 m/s^2 (use the gravity preset), and choose which other variable you know - typically displacement (height fallen) or time. The calculator fills in the rest. Take care with signs: if you define downward as positive, displacement and acceleration are both positive for a falling object.
Does this work for horizontal deceleration, like braking?
Yes. Enter the initial speed as u, enter 0 for v (object comes to rest), leave s and t blank. Provide the deceleration as a negative number (since it opposes motion) or let the solver derive it from additional known values. The result gives stopping distance and stopping time.
What is the difference between displacement and distance?
Displacement is the straight-line vector from start to end position and can be negative if the object moved backward. Distance is the total path length, which is always positive. SUVAT calculates displacement. If the object reverses direction during the interval, displacement will be smaller than distance travelled - you would need to split the interval at the turning point to find total distance.
Can SUVAT be used for vertical and horizontal motion separately in projectile problems?
Yes - that is exactly how two-dimensional projectile motion is solved. Horizontal: u_x = v_x (no acceleration), so s_x = u_x x t. Vertical: apply SUVAT with a = 9.807 m/s^2 downward. The two components share the same time of flight. Solve the vertical SUVAT for t, then use it in the horizontal component.