Acceleration Calculator
Acceleration from velocity change and time.
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Acceleration is how quickly velocity changes. Enter an initial velocity, final velocity, acceleration, or time — any three — and this calculator finds the fourth using v = u + a·t, along with the distance travelled.
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Acceleration — The Quick Answer
Acceleration equals the change in velocity divided by the time taken: a = (v − u) ÷ t, in metres per second squared. A positive value speeds up; a negative value slows down.
Shortcut
a = (v − u) ÷ t | v = u + a·t | u = v − a·t | t = (v − u) ÷ a
The SUVAT quantities (constant acceleration)
| Symbol | Quantity | Unit |
|---|---|---|
| u | Initial velocity | m/s |
| v | Final velocity | m/s |
| a | Acceleration | m/s² |
| t | Time | s |
| s | Displacement | m |
On Earth, free-falling objects accelerate at about 9.81 m/s² due to gravity. A car going 0–100 km/h in 5 seconds averages roughly 5.6 m/s².
How It Works
The Formula
The first equation of motion
Formula
v = u + a·t a = (v − u) / t u = v − a·t t = (v − u) / a
Variables
Acceleration
Rate of change of velocity, in m/s². Positive speeds up, negative slows down (deceleration).
Initial and final velocity
Velocity at the start (u) and end (v) of the time interval, in m/s.
Time
The duration over which the velocity changes, in seconds.
Note: This uses the first equation of motion and assumes constant acceleration. The displacement shown uses s = ½(u + v)·t, which is exact for uniform acceleration.
Worked Example: A Car Speeding Up
From 10 m/s to 30 m/s in 4 seconds
Note the known values
u = 10 m/s, v = 30 m/s, t = 4 s
Apply a = (v − u) ÷ t
(30 − 10) ÷ 4
Compute the acceleration
= 5 m/s²
Find displacement with s = ½(u + v)t
½ × 40 × 4 = 80 m
Reference Guide
| Solve for | Formula | Unit |
|---|---|---|
| Acceleration (a) | a = (v − u) ÷ t | m/s² |
| Final velocity (v) | v = u + a × t | m/s |
| Initial velocity (u) | u = v − a × t | m/s |
| Time (t) | t = (v − u) ÷ a | seconds |
Reading the Result Correctly
Speed vs acceleration, and signs
A car cruising at a steady 70 mph has zero acceleration — nothing is changing. A sprinter leaving the blocks has huge acceleration while barely moving. Acceleration measures how quickly velocity changes, not how fast you're going.
Best for: Separating speed from acceleration
A minus sign means the object is decelerating, or accelerating in the opposite direction to the one you called positive. Keep your sign convention consistent through a problem and the arithmetic stays right.
Best for: Handling braking and direction correctly
Near Earth, free fall accelerates everything at about 9.81 m/s² regardless of mass (ignoring air resistance). After one second a faller moves at ~10 m/s, after two ~20 m/s — which is why falls get dangerous fast.
Best for: Applying the formula to falling objects
What Is Acceleration?
Acceleration is the rate at which velocity changes over time, calculated as the change in velocity divided by the time taken (a = (v − u) ÷ t) and measured in metres per second squared. The crucial point is that it's about change, not current speed: steady motion means zero acceleration, even at high speed, while a rapidly changing velocity means high acceleration even near a standstill. For constant acceleration, the equation v = u + a·t links initial velocity, acceleration, time, and final velocity, and this calculator also returns the displacement. Near Earth, gravity accelerates falling objects at about 9.81 m/s² regardless of their mass.
Key Features
💡 Pro Tips
- →Decide which direction is positive before you start, and keep it consistent — that's what makes negative (deceleration) values come out right.
- →This tool assumes constant acceleration; for changing acceleration you need calculus or step-by-step intervals.
- →For free fall, set the acceleration to 9.81 m/s² (ignoring air resistance).
- →Watch units — convert km/h to m/s (divide by 3.6) before entering velocities.
Common Mistakes
Confusing acceleration with speed
High speed with no change means zero acceleration. Treating 'fast' as 'accelerating' misreads the physics — acceleration is the rate of change of velocity.
Dropping the sign convention
Deceleration is negative acceleration relative to your chosen positive direction. Switching conventions mid-problem produces wrong, often impossible, answers.
Mixing km/h with m/s
The equations use metres per second. Entering a velocity in km/h without converting (divide by 3.6) throws the result off by a factor of 3.6.
Research & Citations
Sources and standards referenced for the factual claims on this page
- [1]
Newton, I. (1687). Philosophiæ Naturalis Principia Mathematica. Royal Society, London.
The foundations of the equations of motion.
View source - [2]
National Institute of Standards and Technology (NIST) (2019). Standard acceleration of gravity (gₙ = 9.80665 m/s²). NIST.gov.
Standard value of gravitational acceleration.
View source
This calculator is a reference tool, not a substitute for professional advice. Verify important health, financial, legal, or safety decisions with a suitably qualified professional.
Last updated: October 7, 2026
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Frequently Asked Questions
How do I calculate acceleration?
Divide the change in velocity by the time taken: a = (v − u) ÷ t. If a car speeds up from 10 m/s to 30 m/s in 4 seconds, its acceleration is (30 − 10) ÷ 4 = 5 m/s².
What are the units of acceleration?
Metres per second squared (m/s²) in SI units — it's a velocity (m/s) changing per second. You may also see g (gravitational units), where 1 g ≈ 9.81 m/s².
What does negative acceleration mean?
Negative acceleration (sometimes called deceleration) means the object is slowing down, or accelerating in the opposite direction to the one you've defined as positive. Keep your sign convention consistent across all values.
How do I find final velocity?
Use v = u + a·t: start with the initial velocity and add the acceleration multiplied by time. Starting at 5 m/s and accelerating at 2 m/s² for 3 seconds gives 5 + 2 × 3 = 11 m/s.