Solve kinematic equations for s, u, v, a, or t
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When you’re working through kinematics problems, tracking five variables across multiple equations can quickly become overwhelming. The SUVAT equations named for the five quantities they relate (displacement s, initial velocity u, final velocity v, acceleration a, and time t) are the backbone of classical mechanics for motion with constant acceleration. This calculator handles the algebra for you, so you can focus on understanding the physics rather than getting stuck on the math.
Enter any four of the five SUVAT variables, choose which one you want to solve for, and the calculator applies the appropriate kinematic equation instantly. Whether you’re a student verifying homework, an educator preparing examples, or an engineer doing quick calculations, this tool simplifies the process. All processing happens locally in your browser, keeping your work private and responsive.
Select the variable you want to solve for displacement (s), initial velocity (u), final velocity (v), acceleration (a), or time (t) using the mode buttons at the top.
Enter values for the other four variables in their respective input fields, leaving the variable you’re solving for either blank or populated (the calculator will overwrite it).
Choose appropriate units for each value, meters or feet for displacement, m/s or mph for velocities, m/s² or ft/s² for acceleration, and seconds or minutes for time.
Click the Calculate button or simply wait for automatic updates the result appears instantly in the highlighted section.
Review the solved value, the equation used, and the input summary to verify your work.
Use the Copy button to save the results or Share to send them to classmates or colleagues.
The calculator applies the five standard equations of motion for constant acceleration, selecting the appropriate one based on which variables you provide and which one you’re solving for. The SUVAT equations are:
Formula: v = u + at (no displacement needed)
Formula: s = ut + ½at² (no final velocity needed)
Formula: v² = u² + 2as (no time needed)
Formula: s = ½(u + v)t (no acceleration needed)
Formula: s = vt − ½at² (no initial velocity needed)
The calculator uses these relationships to solve for the unknown variable. For example, when solving for displacement (s) with u, a, and t known, it applies s = ut + ½at². When solving for time (t) with s, u, and a known, it solves the quadratic equation using the discriminant. The tool handles all unit conversions internally all inputs are converted to base SI units (meters, meters per second, meters per second squared, seconds) before computation, then converted back to the selected output unit for display.
A car accelerates from 10 m/s with a constant acceleration of 2 m/s² for 5 seconds over a displacement of 100 meters. What is the final velocity?
Step 1: Select the variable to solve for
Choose “v” from the mode buttons.
Step 2: Enter the known values
Displacement (s): 100 m
Initial velocity (u): 10 m/s
Acceleration (a): 2 m/s²
Time (t): 5 s
Step 3: Calculate
The calculator applies v = u + at:
v = 10 + (2 × 5) = 20 m/s
Step 4: Interpret the result
The car reaches 20 m/s after 5 seconds. This matches the physics: acceleration increases speed by 2 m/s each second, so from 10 m/s the car gains 10 m/s over 5 seconds, reaching 20 m/s. The displacement check would be s = ut + ½at² = 10×5 + ½×2×25 = 50 + 25 = 100 m, confirming consistency.
A car is traveling at 25 m/s when the driver applies the brakes, producing a constant deceleration of 5 m/s². How far does the car travel before stopping, and how long does it take?
Known values: u = 25 m/s, v = 0 m/s (stopped), a = −5 m/s² (deceleration), unknown s and t.
Step 1: Find stopping distance
Use v² = u² + 2as:
0² = 25² + 2×(−5)×s
0 = 625 − 10s
s = 62.5 meters
Step 2: Find stopping time
Use v = u + at:
0 = 25 + (−5)×t
t = 5 seconds
Interpretation: The car travels 62.5 meters over 5 seconds — a useful calculation for road safety and vehicle design.
Eliminates tedious algebra and arithmetic errors in kinematics problem-solving.
Handles all five SUVAT variables with automatic unit conversion between multiple measurement systems.
Provides instant results that update as you change inputs — perfect for exploring “what if” scenarios.
Shows the equation used and the input values, building confidence in the result.
Runs entirely client-side with no data transmission, keeping your work completely private.
Displays solved results directly in the input field with visual feedback (green highlight).
Works on any device with responsive design, from phones to desktops.
SUVAT is an acronym for the five variables in the kinematic equations: s (displacement), u (initial velocity), v (final velocity), a (acceleration), and t (time). It’s a memory aid used in physics education, particularly in the UK and other English-speaking countries.
Choose the equation based on which variables are known and which is unknown. v = u + at omits s, s = ut + ½at² omits v, v² = u² + 2as omits t, s = ½(u+v)t omits a, and s = vt − ½at² omits u. Select the equation that includes your unknown and all known variables.
If acceleration is zero (uniform motion), the equations simplify. v = u (velocity is constant), s = ut (or s = vt), and the other equations reduce to these forms. The calculator handles this case automatically.
Yes — SUVAT equations apply to any motion with constant acceleration, including vertical free-fall. For falling objects, a = g = 9.81 m/s² downward (positive downward or negative upward depending on your sign convention). Just be consistent with direction signs.
Displacement (s) is a vector quantity — it’s the straight-line distance from the start point to the end point, with direction. Distance is the total path length traveled, which may be longer. SUVAT equations use displacement, which can be negative if motion is in the negative direction.
Negative acceleration (deceleration) simply means acceleration acts opposite to the direction of motion. Enter it as a negative value. The equations work the same way — just be careful with signs. For example, braking is negative acceleration relative to the car’s motion.
If a = 0 and you need to solve for t, the equation v = u (velocity constant) doesn’t involve t. Instead, use s = ut to find t = s/u, provided u ≠ 0. If u = 0 and a = 0, the object isn’t moving — time is undefined for displacement.
When solving for time with non-zero acceleration, the calculator uses the quadratic formula. If the discriminant (u² + 2as) is negative, there’s no real solution — meaning the given inputs cannot occur physically under constant acceleration. This often indicates inconsistent values or sign errors.
The calculator supports meters, kilometers, feet, and yards for displacement; m/s, km/h, mph, and ft/s for velocities; m/s² and ft/s² for acceleration; and seconds and minutes for time. All values are internally converted to SI units for consistency.
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