The Acceleration Calculator finds constant acceleration from a change in velocity over time, from the rearrangement of v² = u² + 2as, or from Newton's second law as force divided by mass. Enter the known values for the mode you need, and the tool returns metres per second squared, with an optional reading as a multiple of standard gravity.
Acceleration is the rate of change of velocity. Braking, free fall and a shove on a known mass are the same quantity in different clothes, and the sign of the result is part of the answer rather than a separate "deceleration" species.
Calculate acceleration from change in velocity
Average acceleration over an interval is final velocity minus initial velocity, divided by the time between them. Under the constant-acceleration assumption used throughout SUVAT, that average is the acceleration at every moment in the interval. Enter u, v and t, and the tool returns a with the arithmetic shown.
a = (v − u) / tThis is the rearrangement of v = u + at. Time must not be zero. A cart that goes from rest to 27 m/s in 9 s:
a = (27 − 0) / 9 = 3 m/s²
Positive a with positive v growing means speeding up in the positive direction. The same formula returns a negative value when velocity falls while the positive direction is held fixed. Unit selectors convert velocity and time to SI before dividing so mixed inputs such as km/h and seconds do not need a manual step.
Calculate acceleration from velocity and displacement
When time is unknown, acceleration still follows from initial velocity, final velocity and displacement. Rearrange v² = u² + 2as for a. Division by twice the displacement is undefined when s = 0; a zero displacement with unequal end velocities cannot fit constant acceleration along that axis for a finite interval.
a = (v² − u²) / (2s)A vehicle that slows from 10 m/s to rest over 25 m:
a = (0² − 10²) / (2 × 25) = (−100) / 50 = −2 m/s²
The negative sign is the braking: velocity was positive and decreasing. Checking with the change-in-velocity form would need the time from another equation; here time never entered. For equation selection across all five SUVAT variables, use the Kinematics Calculator.
Calculate acceleration from force and mass
Newton's second law states that net force equals mass times acceleration. Solving for acceleration gives force divided by mass. This mode is not a kinematic rearrange; it links the motion to the cause of the acceleration when a constant net force acts on a known mass.
F = ma
a = F / mA net force of 30 N on a 10 kg mass:
a = 30 / 10 = 3 m/s²
Mass must be in kilograms and force in newtons for a in m/s². A force of zero yields zero acceleration. Direction of a matches the direction of the net force. Friction and other opposing forces belong in the net force before you divide; entering only the applied push while a friction force remains unbalanced produces an acceleration the object never has. Related force problems sit on the Friction Calculator once that page is live.
Find acceleration for u = 0, v = 27, t = 9
An object starts from rest and reaches 27 m/s after 9 seconds of steady speeding up. The acceleration is 3 m/s². Those three inputs are the worked fixture for this page, so every step below is what the tool must reproduce when the change-in-velocity mode is selected with the same numbers.
1. List what is known. u = 0 m/s, v = 27 m/s, t = 9 s. Displacement is not required.
2. Apply the equation. a = (v − u) / t
3. Substitute. a = (27 − 0) / 9
4. Solve. a = 3 m/s²
Displacement for the same interval, for a consistency check:
s = ½(u + v)t = ½(0 + 27) × 9 = ½ × 27 × 9 = 121.5 m
Or from s = ut + ½at²:
s = 0 + ½ × 3 × 81 = 121.5 m
As a multiple of standard gravity:
3 / 9.80665 ≈ 0.306 g
The same 3 m/s² from force and mass uses F = 30 N and m = 10 kg, because 30 / 10 = 3. Three routes (velocity change, kinematics check on displacement, and F / m) land on one acceleration when the inputs describe the same motion.
Understand deceleration as negative acceleration
Deceleration in everyday speech means slowing down. In the equations, that situation is simply acceleration with a sign opposite the velocity. There is no separate physical quantity called deceleration with its own unit; the calculator reports a signed a and a note when velocity and acceleration point opposite ways.
A bike moving at +15 m/s that loses speed under a = −2 m/s² is decelerating in ordinary language and has negative acceleration in the algebra. An object moving at −15 m/s (the negative direction) that has a = −2 m/s² is speeding up while both quantities are negative. Slowing down always means acceleration opposite velocity; the word "deceleration" alone does not fix the sign without knowing which way the object is travelling.
Braking distance problems therefore enter a negative a when the positive axis follows the initial motion. Writing "deceleration = 2 m/s²" in a notebook is fine as a description; substituting into SUVAT still needs a = −2 under that axis choice.
The Velocity Calculator returns the signed v that pairs with this a. When velocity and acceleration have opposite signs, speed falls; when they share a sign, speed rises. That single comparison replaces a separate deceleration switch on the form.
Express acceleration in g-forces
A g-force reading is acceleration divided by standard gravity. Standard gravity is defined as exactly 9.80665 m/s². Dividing the signed or absolute value of a by that constant states how many multiples of free-fall acceleration the object experiences, which is how aviation, motorsport and crash reports quote peaks.
n_g = a / 9.80665For a = 3 m/s²:
n_g = 3 / 9.80665 ≈ 0.306
For free fall itself, |a| = 9.80665 m/s² and the magnitude is 1 g. Aviation, motorsport and crash testing quote peaks in g because the number compares directly to weight: 2 g means a net acceleration twice what standing on Earth feels from gravity alone. The tool can show both m/s² and the g multiple. Local gravitational acceleration varies slightly over the Earth's surface; the conversion here always uses the standard value 9.80665, not a local survey figure.
A negative acceleration of −3 m/s² is −0.306 g on the same scale. Reports sometimes quote the absolute multiple and name the direction in words (braking, downward). Either presentation is fine if the sign convention for the axis stays visible next to the number.
Frequently asked questions
Acceleration questions usually ask how to form a from velocities and time, how braking relates to a minus sign, and how a result in m/s² converts into a multiple of g. Each answer below restates the question first, then gives the formula or convention, using the fixture a = 3 m/s² where a concrete number clarifies the point.
How do you calculate acceleration from velocity and time?
Subtract initial velocity from final velocity, then divide by time: a = (v − u) / t. With u = 0, v = 27 m/s and t = 9 s, a = 3 m/s².
How do you find acceleration without time?
Use a = (v² − u²) / (2s). The form comes from v² = u² + 2as. It needs a nonzero displacement.
What is the formula linking force and acceleration?
Newton's second law: F = ma, so a = F / m. A 30 N net force on 10 kg produces 3 m/s².
Is deceleration different from negative acceleration?
Deceleration describes slowing down in ordinary language. In the equations, slowing down is acceleration opposite the velocity. The reported value is still a signed acceleration in m/s², not a second kind of quantity.
Can acceleration be negative while speed increases?
Yes. If velocity is already negative and acceleration is also negative, speed (the magnitude) rises. Sign tracks direction relative to the axis, not whether the ride feels faster.
What does a reading of 1 g mean?
It means the acceleration magnitude equals standard gravity, 9.80665 m/s². Free fall near Earth without air resistance is 1 g. A result of 0.306 g for a = 3 m/s² is just 3 divided by 9.80665.
What units does acceleration use?
The SI unit is metres per second squared (m/s²). Feet per second squared appear in some imperial texts; convert with the factor 0.3048 m per foot before solving in SI, or select that unit on the field. Multiples of g are a display choice on top of m/s².
Why must time be nonzero in a = (v − u)/t?
Division by zero is undefined. If two velocities are recorded at the same instant, you do not have an interval over which to define average acceleration from those samples.
Does constant acceleration mean constant force?
For fixed mass, yes: F = ma makes constant a and constant net F the same statement. If mass changes (a rocket burning fuel) or net force changes, acceleration is not constant and SUVAT does not apply over that whole interval.
How does this relate to the velocity and displacement tools?
The Velocity Calculator solves for v. The Displacement Calculator solves for s. This page solves for a from the matching rearrangements and from F / m. All three share the constant-acceleration assumption.
Summary
Constant acceleration follows from (v − u) / t, from (v² − u²) / (2s), and from F / m. The worked case u = 0, v = 27 m/s, t = 9 s gives a = 3 m/s², about 0.306 g using standard gravity 9.80665 m/s².
Deceleration is not a separate unit; it is signed acceleration opposite the motion. Force mode needs net force and mass in SI so the result lands in m/s².