SUVAT Calculator
Solve SUVAT kinematics equations for displacement, velocity, acceleration, and time with step-by-step breakdown.
What Are SUVAT Equations?
SUVAT equations describe motion with constant acceleration. The letters stand for displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t). Given any four values, you can solve for the fifth using one of five standard kinematic formulas.
The Five SUVAT Formulas
$$v = u + at$$ $$s = ut + \frac{1}{2}at^2$$ $$s = vt - \frac{1}{2}at^2$$ $$v^2 = u^2 + 2as$$ $$s = \frac{1}{2}(u + v)t$$Example: a car starts at 5 m/s, accelerates at 2 m/s² for 5 s. Final velocity is \(v = 5 + 2 \times 5 = 15\) m/s and displacement is \(s = 5 \times 5 + 0.5 \times 2 \times 25 = 50\) m.
When to Use Each Equation
Pick the equation that does not require the unknown variable. If time is missing, use \(v^2 = u^2 + 2as\). If acceleration is missing, use \(s = \frac{1}{2}(u + v)t\). Our calculator selects the compatible formula automatically based on your inputs.
Related tools: Projectile Motion Calculator and Free Fall Calculator.
Frequently Asked Questions
What does each letter in SUVAT mean?
s is displacement in meters, u is initial velocity, v is final velocity, a is constant acceleration, and t is elapsed time. All velocities and acceleration use consistent SI units.
Can SUVAT handle negative acceleration?
Yes. Negative acceleration means deceleration. Displacement and velocity can also be negative when direction matters, as long as all values use the same sign convention.
Why do I get two answers for velocity sometimes?
When using \(v^2 = u^2 + 2as\), the square root gives a magnitude. In most forward-motion problems, take the positive root. Reverse motion may need the negative value.
Do SUVAT equations work for projectile motion?
They work separately for horizontal and vertical components when acceleration is constant. Gravity gives \(a = -g\) vertically while horizontal acceleration is often zero.
What if acceleration is not constant?
SUVAT only applies to uniform acceleration. Variable acceleration needs calculus or numerical integration instead of these algebraic formulas.
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