⚡ Enter any 3 known values — leave the unknown field(s) empty. The calculator solves using SUVAT equations.
m
Positive = forward, negative = backward
m/s
Velocity at start (0 if at rest)
m/s
Velocity at end (0 if stops)
m/s²
Negative for deceleration
s
Duration in seconds
Set gravitational acceleration
Solved Variables
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Sources & Methodology
SUVAT equations verified against NIST SI unit standards, Khan Academy physics curriculum, and The Physics Classroom reference materials.
NIST Special Publication 811 — SI Units Guide
Reference for SI unit definitions: metres (displacement), m/s (velocity), m/s² (acceleration), and seconds (time)
Khan Academy — One-Dimensional Motion and Kinematics
Reference for SUVAT equation derivations, worked examples, and uniform acceleration problem-solving methodology
The Physics Classroom — 1D Kinematics
Cross-reference for equation selection strategy, sign convention, and real-world application examples
Methodology: The solver identifies which of s, u, v, a, t are provided and which are blank. It tries each of the four SUVAT equations and solves algebraically for the unknown. Quadratic cases (t from s = ut + ½at²) use the quadratic formula; both roots are evaluated and the physically meaningful solution (non-negative t) is returned. All computations use SI units and IEEE 754 double-precision arithmetic. Results are rounded to 4 significant figures for display.
⏱ Last reviewed: April 2026
SUVAT Kinematic Equations — How to Solve UAM Problems
Uniformly Accelerated Motion (UAM) describes any object moving with constant acceleration. The four SUVAT equations relate five variables: displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t). Knowing any three allows you to solve for the remaining two.
The 4 SUVAT Equations
Eq. 1: v = u + at
Velocity-time equation. Use when s is not needed. Example: Car from rest at 2 m/s² for 5 s → v = 0 + 2×5 = 10 m/s
Eq. 2: s = ut + ½at²
Displacement-time equation. Use when v is not needed. Example: s = 0×5 + ½×2×25 = 25 m
Eq. 3: v² = u² + 2as
Velocity-displacement equation. Use when t is not needed. Example: v² = 0 + 2×2×25 = 100 → v = 10 m/s
Eq. 4: s = ½(u + v)t
Average velocity equation. Use when a is not needed. Example: s = ½×(0+10)×5 = 25 m
SUVAT Variable Reference
| Symbol | Variable | SI Unit | Sign Convention |
|---|---|---|---|
| s | Displacement | metres (m) | + = forward/up, − = backward/down |
| u | Initial velocity | m/s | 0 if object starts at rest |
| v | Final velocity | m/s | 0 if object comes to rest |
| a | Acceleration | m/s² | −9.81 for free fall downward |
| t | Time | seconds (s) | Always positive or zero |
Worked Example — Braking Car
A car travels at 20 m/s and brakes with deceleration 5 m/s². Find stopping distance and stopping time.
Known: u = 20 m/s, v = 0 (stops), a = −5 m/s². Unknown: s and t.
Using Eq. 3: v² = u² + 2as → 0 = 400 + 2(−5)s → 10s = 400 → s = 40 m
Using Eq. 1: v = u + at → 0 = 20 + (−5)t → 5t = 20 → t = 4 s
Worked Example — Free Fall
A ball is dropped from rest. How far does it fall in 3 seconds?
Known: u = 0, a = −9.81 m/s², t = 3 s. Unknown: s and v.
Using Eq. 2: s = 0×3 + ½(−9.81)(9) = −44.1 m (44.1 m downward)
Using Eq. 1: v = 0 + (−9.81)(3) = −29.4 m/s (downward)
💡 Sign Convention Tip: Be consistent — pick one direction as positive throughout the problem. For projectiles thrown upward, set up = positive, so a = −9.81 m/s² and the object's initial velocity is positive. Getting signs wrong is the most common source of errors in kinematics.
Frequently Asked Questions
Uniformly accelerated motion (UAM) is motion where acceleration remains constant throughout. Velocity changes by the same amount every second. Free fall under gravity at 9.81 m/s² is the most common example. The four SUVAT equations describe all aspects of UAM completely.
The four SUVAT equations are: (1) v = u + at, (2) s = ut + ½at², (3) v² = u² + 2as, (4) s = ½(u+v)t. Where s = displacement, u = initial velocity, v = final velocity, a = acceleration, t = time. Each equation contains four of the five variables and is selected based on which three variables are known.
SUVAT stands for the five kinematic variables: S = displacement (m), U = initial velocity (m/s), V = final velocity (m/s), A = acceleration (m/s²), T = time (s). Given any three of these five values, the remaining two can always be calculated using the four SUVAT equations.
Identify the three known variables and one unknown. Choose the equation that contains all three knowns and the unknown. For example: if u, a, t are known and v is unknown, use v = u + at. If u, v, a are known and s is unknown, use v² = u² + 2as. This calculator automates equation selection — just enter three values and it solves automatically.
The standard acceleration due to gravity on Earth's surface is 9.81 m/s². When modelling free fall downward (taking up as positive), use a = −9.81 m/s². The value varies slightly by location — 9.832 m/s² at the poles and 9.780 m/s² at the equator. Use the +9.81 and −9.81 buttons in this calculator to fill in gravity instantly.
Yes. Deceleration is simply negative acceleration — enter a negative value for a. For a braking car, a might be −5 m/s². Velocity decreases over time as expected. For an object stopping completely, set v = 0 and solve for stopping distance or stopping time using the appropriate equation.
Displacement is the straight-line change in position from start to end, including direction. It is a vector — positive forward or upward, negative backward or downward. It differs from total distance: if an object moves 10 m forward then 10 m back, displacement is 0 but total distance is 20 m.
SUVAT equations only apply when acceleration is constant. They fail when acceleration varies (e.g. due to air resistance or variable force). For variable acceleration, calculus-based kinematics using integration is required. In practice, gravity causes near-constant acceleration over typical problem distances, making SUVAT highly accurate for most physics and engineering problems.
Time can be found using v = u + at, giving t = (v − u) / a when v, u, a are known. Alternatively, s = ½(u + v)t gives t = 2s / (u + v) when s, u, v are known. The equation s = ut + ½at² gives a quadratic in t requiring the quadratic formula when s, u, a are known.
Projectile motion is treated as two independent UAMs: horizontal (zero acceleration, constant velocity) and vertical (constant downward acceleration of 9.81 m/s²). SUVAT equations are applied separately to each direction. Horizontal range, maximum height, and time of flight are all found using SUVAT applied to the vertical dimension.
Final velocity uses v = u + at when time is known, or v² = u² + 2as when displacement is known but time is not. For example: a car from rest at 3 m/s² for 5 s gives v = 0 + 3×5 = 15 m/s. After travelling 37.5 m: v² = 0 + 2×3×37.5 = 225, so v = 15 m/s confirming the result.
Use v² = u² + 2as with final velocity v = 0. Rearranging: s = −u² / (2a), where a is the negative deceleration. For a car at 20 m/s braking at −5 m/s²: s = −400 / (2 × −5) = −400 / −10 = 40 metres stopping distance. Enter these values in this calculator for an instant result.
SI units are standard: displacement in metres (m), velocity in m/s, acceleration in m/s², time in seconds (s). Always convert to SI before calculating. To convert km/h to m/s divide by 3.6. To convert miles per hour, multiply by 0.447. All equations and results on this calculator use SI units.
Yes. Rotational analogues replace displacement with angular displacement (θ), initial velocity with initial angular velocity (ω₀), final velocity with ω, and acceleration with angular acceleration (α). The four equations have identical forms. This calculator solves linear UAM only; for rotational kinematics, substitute the equivalent angular variables.
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