Use this SUVAT calculator to solve straight-line motion with constant acceleration from any 3 known values and see the equation steps, sign convention, and any valid time roots.
Advanced options
How to use our SUVAT Calculator
- Choose Solve mode. Use Any 3 known values if you want the calculator to solve as much as possible, or use target mode if you want one variable first.
- If you use target mode, pick the unknown in Target variable and leave that variable's input box blank.
- Select Unit system before entering numbers. Keep every input in the displayed units.
- Set Positive direction convention. After that, any motion in the opposite direction should be entered as a negative value for Displacement, s, Initial velocity, u, Final velocity, v, or Acceleration, a.
- Enter the known values for s, u, v, a, and t. In any-3 mode, enter at least 3 known values and leave unknown boxes blank.
- Use Advanced options if needed. Time-root policy controls how multiple valid time answers are shown, and Number display format changes how results are written.
- Click Calculate, then read Equation(s) used to see which SUVAT relationship was chosen and how your numbers were substituted.
- Sanity-check the result: make sure Time, t is not negative, the signs match your chosen direction, and Solution notes does not warn that the inputs are inconsistent or outside straight-line constant-acceleration motion.
Definitions
SUVAT: A set of 5 variables used for straight-line motion with constant acceleration: displacement s, initial velocity u, final velocity v, acceleration a, and time t [1].
Displacement, s: Change in position from start to finish. It can be positive or negative depending on your chosen direction.
Initial velocity, u: The velocity at the start of the motion interval.
Final velocity, v: The velocity at the end of the motion interval.
Acceleration, a: How quickly velocity changes. This calculator assumes it stays constant for the whole interval [1].
Time, t: Elapsed time from the chosen start moment. This calculator only accepts non-negative time.
Positive direction convention: Your sign rule, such as forward/up is positive. Negative values mean the opposite direction.
Time-root policy: A setting for cases where solving for time gives more than one real answer.
Standard gravity: The standard acceleration of gravity is 9.80665 m/s^2 when used as an optional helper value [2].
Common mistakes and quick fixes
Mistake: Choosing a target in Target variable but also typing a value for that same variable.
Fix: Clear the target variable's input box, or switch to Any 3 known values mode.
Mistake: Changing Unit system and then entering numbers in old units, such as typing km/h when the box is showing m/s.
Fix: Convert your values first and enter everything in the displayed units only.
Mistake: Forgetting the sign convention after choosing the positive direction.
Fix: Check Solve mode and then recalculate. Enter negative displacement, velocity, or acceleration whenever the motion points opposite your chosen positive direction.
Mistake: Entering a negative value for Time, t .
Fix: Use elapsed time only. Enter 0 or a positive value, or leave time blank if it is the unknown.
Mistake: Trying to solve with too little information, such as only two known motion values.
Fix: Check Solve mode and then recalculate. In any-3 mode, enter at least 3 known values among s , u , v , a , and t .
Mistake: Assuming two time answers must mean the calculator failed.
Fix: Read Solution notes . Two non-negative roots can be physically possible and may represent reaching the same displacement at two different times.
Limitations & Key Assumptions / Boundary Conditions
This calculator only works for 1D motion, which means motion along one straight line. It does not directly solve 2D motion, curved paths, or projectile motion unless you first split the motion into separate components.
It assumes Acceleration, a is constant for the whole time interval. If acceleration changes during the motion, the SUVAT equations may not match the real motion.
Time, t must be 0 or greater. Negative time roots are excluded even if they appear in the algebra.
If you enter more than 3 known values, the calculator treats them as one motion interval and checks whether they agree within a small rounding tolerance. Real measured data may differ slightly because of measurement error or rounding.
When two non-negative time roots exist, both may be mathematically valid. You still need the context of the problem to decide which branch describes the real event.
If Acceleration, a equals 0, the calculator switches to constant-velocity relationships instead of formulas that divide by acceleration.
Methodology
The solver first checks which of the 5 SUVAT values are known: Displacement, s, Initial velocity, u, Final velocity, v, Acceleration, a, and Time, t. It then chooses a constant-acceleration equation that matches the missing variable [1].
v = u + a*t
s = u*t + 0.5*a*t^2
v^2 = u^2 + 2*a*s
s = 0.5*(u + v)*t
s = v*t - 0.5*a*t^2
The selected Positive direction convention controls the sign of every input and output. A negative displacement, velocity, or acceleration means that quantity points opposite the chosen positive direction, and the solver uses those signed values exactly as entered.
If time is unknown, the solver may need a quadratic equation. It checks the discriminant first. If the discriminant is negative, there is no real solution under constant acceleration.
t = (-u +/- sqrt(u^2 + 2*a*s)) / a
If both roots are real and non-negative, the calculator can show both. This matters because the same displacement can sometimes be reached at two different times during one constant-acceleration motion.
If Acceleration, a is 0, the solver avoids divide-by-zero and uses the constant-velocity fallback instead.
if a = 0, then v = u and s = u*t
If you enter extra known values, the calculator compares them with the solved values using a small tolerance. If they agree within rounding tolerance, they are treated as consistent. If not, the calculator reports an inconsistency instead of forcing a wrong answer.
A quick example: if u = 0 m/s, a = 2 m/s^2, and t = 5 s, then the first equation gives v = 0 + 2*5 = 10 m/s. Next, the second equation gives s = 0*5 + 0.5*2*25 = 25 m. So the motion ends with final velocity 10 m/s and displacement 25 m.
The method is valid only for straight-line motion with constant acceleration [1]. If the motion changes direction in a more complex way, uses changing acceleration, or needs 2D components, real results can differ. If a gravity helper is used, the standard value is 9.80665 m/s^2 [2].