100
m
0
m/s
20
m/s
2
m/s²
10
s
2
100
m
0
m/s
20
m/s
2
m/s²
10
s
2
The Uniformly Accelerated Motion Calculator (also known as the SUVAT Calculator) solves the five standard kinematic equations of motion for any unknown variable. SUVAT stands for the five variables of uniformly accelerated motion: S (displacement), U (initial velocity), V (final velocity), A (acceleration), and T (time). Given any three of these variables, you can find the remaining two.
The SUVAT equations are the workhorse formulas of classical kinematics. They describe motion in a straight line with constant acceleration, which is one of the most common types of motion encountered in physics. These five equations are derived from the definitions of velocity and acceleration through simple algebra and calculus, yet they are powerful enough to solve a vast range of real-world problems.
This calculator lets you select which variable to solve for, then enter the values of the other variables. It applies the appropriate SUVAT equation and returns all five values along with an indication of which equation was used. This makes it an ideal tool for physics students learning kinematics, as well as for engineers and scientists who need quick solutions to motion problems.
The five SUVAT equations are: (1) v = u + at, (2) s = ut + ½at², (3) s = vt – ½at², (4) v² = u² + 2as, and (5) s = ½(u + v)t. Each equation connects a different combination of four variables, omitting one. By choosing the equation that excludes the variable you do not know (other than the one you are solving for), you can find your answer with just three known values.
Uniformly accelerated motion applies to many real scenarios: vehicles accelerating or braking on straight roads, objects falling under gravity (constant a = g), elevators starting and stopping, trains on straight tracks, and projectiles during free flight (in one dimension). Even in cases where acceleration is not perfectly constant, the SUVAT equations provide useful first-order approximations.
Understanding and mastering the SUVAT framework is a critical foundation for more advanced topics in mechanics, including two-dimensional projectile motion, circular motion, and eventually Newton’s laws and energy methods. This calculator serves both as a learning aid and a practical problem-solving tool.
The calculator uses five standard SUVAT (kinematic) equations of uniformly accelerated motion:
Equation 1 (finding v):
$$v = u + at$$
Equation 2 (finding s):
$$s = ut + \frac{1}{2}at^2$$
Equation 3 (finding u from v, a, t):
$$u = v - at$$
Equation 4 (finding a from s, u, v):
$$v^2 = u^2 + 2as \implies a = \frac{v^2 - u^2}{2s}$$
Equation 5 (finding t from u, v, a):
$$t = \frac{v - u}{a}$$
Depending on which variable you choose to solve for, the calculator applies the appropriate equation using the remaining known values. All inputs use SI units (meters, seconds, m/s, m/s²).
The results display all five SUVAT variables, with the solved value highlighted. Positive displacement means motion in the positive direction. Positive velocity means movement in the positive direction. Positive acceleration means speeding up in the positive direction (or slowing down in the negative direction). A negative time result indicates the chosen set of values may not be physically consistent—check your inputs in that case.
Inputs
Results
A car traveling at 30 m/s (108 km/h) brakes with a deceleration of 6 m/s². Using s = ut + ½at², the braking distance is 75 meters over 5 seconds.
Inputs
Results
A sprinter starts from rest and covers 50 m while reaching 10 m/s. Using v² = u² + 2as, the acceleration is 1 m/s².
SUVAT is an acronym for the five variables of uniformly accelerated motion: S (displacement), U (initial velocity), V (final velocity), A (acceleration), and T (time). The term is widely used in British physics education but the equations are universal in classical mechanics worldwide.
You need to know three of the five variables to find the other two. Each SUVAT equation relates four of the five variables, so with three known values you can always find the fourth, and from there the fifth.
A negative time result usually means the combination of inputs is not physically consistent—the motion described cannot occur with those specific values. Double-check that your initial and final velocities, acceleration, and displacement are consistent with each other. In some mathematical contexts, a negative time indicates the event occurred before the reference time t = 0.
Yes. For vertical motion under gravity, set the acceleration to +9.81 m/s² (downward positive) or –9.81 m/s² (upward positive). Free fall, thrown objects, and elevator problems all use the same SUVAT equations with a = ±g.
The calculator uses SI units (meters, seconds, m/s, m/s²). If your values are in other units (km/h, feet, etc.), convert them to SI before entering. For example, 100 km/h = 27.78 m/s. All output values will be in SI units as well.
The SUVAT equations strictly apply only to constant (uniform) acceleration. If acceleration varies, you must use calculus (integration of a(t) to find v(t) and then x(t)) or numerical methods. However, SUVAT equations can give reasonable approximations for short time intervals even when acceleration varies slowly.
Roboculator Team
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