⚡ Free Physics Tool
Free Acceleration Solver — SUVAT, Force & Circular Motion Calculator
Solve any acceleration problem instantly — find acceleration, force, velocity, displacement or time using SUVAT equations, Newton's Second Law, and circular motion formulas. Full step-by-step working shown. No sign-up, completely free.
Acceleration Solver — Select calculation type below
a = (v − u) ÷ t | v = final velocity, u = initial velocity, t = time
Acceleration
—
m/s²
In g-force
—
× 9.81 m/s²
Direction
—
accel/decel
Δ Velocity
—
m/s change
Acceleration vs Deceleration: Positive acceleration means speeding up. Negative acceleration (deceleration/retardation) means slowing down. Zero acceleration means constant velocity.
F = m × a | a = F ÷ m | m = F ÷ a
Result
—
—
In g-force
—
g
Weight Force
—
N (m × 9.81)
Newton's Second Law: Force = Mass × Acceleration. The SI unit of force is the Newton (N). 1 N = 1 kg·m/s². Weight = mass × 9.81 m/s² (gravitational acceleration on Earth).
v=u+at | s=ut+½at² | v²=u²+2as | s=(u+v)/2×t
Enter any 3 known values — leave the 2 unknowns blank. The solver will find them.
SUVAT only works for uniform (constant) acceleration. s=displacement, u=initial velocity, v=final velocity, a=acceleration, t=time. All units must be SI (metres, m/s, m/s², seconds).
Free fall: a = g = 9.81 m/s² | v = g×t | s = ½g×t²
Result
—
—
Time
—
seconds
Distance
—
meters
Final Velocity
—
m/s
Free fall assumes no air resistance. g = 9.81 m/s² on Earth. Objects in free fall accelerate at the same rate regardless of mass (Galileo's principle).
Centripetal a = v² ÷ r = ω²r | F = mv²/r | v = 2πr/T
Centripetal Accel
—
m/s²
Centripetal Force
—
Newtons
Angular Velocity
—
rad/s
Period
—
seconds
Centripetal acceleration always points toward the center of the circle. It is not a new force — it is provided by tension, gravity, friction, or normal force depending on the scenario.
Step by Step
How to solve acceleration problems
Basic acceleration formula
Acceleration is the rate of change of velocity. It measures how quickly an object speeds up, slows down, or changes direction.
a = (v − u) ÷ t
Example: A car accelerates from 0 to 30 m/s in 10 seconds
a = (30 − 0) ÷ 10 = 3 m/s²
In g-force: 3 ÷ 9.81 = 0.306g
In g-force: 3 ÷ 9.81 = 0.306g
Newton's Second Law — F = ma
Force equals mass times acceleration. Rearrange to find any of the three variables.
F = m × a | a = F ÷ m | m = F ÷ a
Example: A 1000 kg car experiences a force of 3000 N
Acceleration = F ÷ m = 3000 ÷ 1000 = 3 m/s²
The four SUVAT equations
SUVAT equations apply to uniform (constant) acceleration only. Enter any 3 known values to find the remaining 2.
v = u + at
Final velocity from initial velocity, acceleration and time. Does not use displacement.
s = ut + ½at²
Displacement from initial velocity, acceleration and time. Does not use final velocity.
v² = u² + 2as
Final velocity from initial velocity, acceleration and displacement. Does not use time.
s = (u+v)/2 × t
Displacement from average velocity and time. Does not use acceleration directly.
Free fall and gravity
v = g×t | s = ½g×t² | v² = 2gs
Example: Object dropped from rest for 3 seconds (g = 9.81 m/s²)
Distance: s = ½ × 9.81 × 3² = 44.1 m
Final velocity: v = 9.81 × 3 = 29.43 m/s
Final velocity: v = 9.81 × 3 = 29.43 m/s
Gravitational acceleration on different planets
| Planet / Body | g (m/s²) | Relative to Earth |
|---|---|---|
| Earth | 9.81 | 1.00g |
| Moon | 1.62 | 0.165g |
| Mars | 3.72 | 0.379g |
| Jupiter | 24.79 | 2.528g |
| Saturn | 10.44 | 1.065g |
| Sun | 274.0 | 27.9g |
Physics Reference
All acceleration & motion formulas
Basic Acceleration
a = (v−u) / t
Change in velocity divided by time. SI unit: m/s²
Newton's 2nd Law
F = m × a
Net force equals mass times acceleration. Unit: Newtons (N)
SUVAT — 1
v = u + at
Final velocity. Known: u, a, t. Missing: s
SUVAT — 2
s = ut + ½at²
Displacement. Known: u, a, t. Missing: v
SUVAT — 3
v² = u² + 2as
Velocity-displacement. Known: u, a, s. Missing: t
SUVAT — 4
s = (u+v)/2 × t
Average velocity × time. Known: u, v, t. Missing: a
Centripetal
a = v² / r
Centripetal acceleration toward center of circular path
Centripetal Force
F = mv² / r
Force required to maintain circular motion
| Symbol | Quantity | SI Unit | Notes |
|---|---|---|---|
| a | Acceleration | m/s² | Positive = speeding up, Negative = slowing down |
| u | Initial velocity | m/s | Velocity at the start of motion |
| v | Final velocity | m/s | Velocity at the end of the time interval |
| s | Displacement | m | Distance in a specific direction |
| t | Time | s | Duration of motion |
| F | Force | N (kg·m/s²) | Net force causing acceleration |
| m | Mass | kg | Amount of matter in an object |
| g | Gravitational accel | 9.81 m/s² | Free fall acceleration on Earth |
| r | Radius | m | Radius of circular path |
| ω | Angular velocity | rad/s | Rate of rotation |
Why Us
Why use this acceleration solver?
⚡
5 solver modes
Basic, F=ma, SUVAT, Free Fall, and Circular Motion — all in one tool, all with full step-by-step solutions.
🧮
Smart SUVAT solver
Enter any 3 of the 5 SUVAT variables — the tool automatically picks the right equation and solves for the rest.
🌍
Multi-planet gravity
Free fall calculations for Earth, Moon, Mars and Jupiter — perfect for planetary physics problems.
📐
Steps always shown
Every result includes the full working — formula selection, substitution, and calculation — so you learn the method.
🔄
Unit conversion built-in
Input velocity in m/s, km/h or mph — time in seconds, minutes or hours. Automatic conversion throughout.
🔓
100% free, no sign-up
No account, no email, no limits. Built for physics students who need accurate answers fast.
FAQ
Frequently asked questions about acceleration
The basic formula for acceleration is: a = (v − u) ÷ t, where v is final velocity, u is initial velocity, and t is time. The SI unit of acceleration is metres per second squared (m/s²). Positive acceleration means speeding up; negative acceleration (deceleration) means slowing down.
The four SUVAT equations for uniform acceleration are: (1) v = u + at, (2) s = ut + ½at², (3) v² = u² + 2as, (4) s = (u+v)/2 × t. SUVAT stands for: s=displacement, u=initial velocity, v=final velocity, a=acceleration, t=time. Enter any 3 values to find the other 2 using our SUVAT solver.
Newton's Second Law states that the net force on an object equals its mass times its acceleration: F = ma. This means: (1) The greater the force, the greater the acceleration. (2) The greater the mass, the smaller the acceleration for the same force. The SI unit of force is the Newton (N), where 1 N = 1 kg·m/s².
The standard gravitational acceleration on Earth is g = 9.81 m/s² (or 9.80665 m/s² precisely). This means that in free fall (ignoring air resistance), an object's velocity increases by 9.81 m/s for every second it falls. On the Moon, g = 1.62 m/s². On Mars, g = 3.72 m/s².
Centripetal acceleration is the acceleration experienced by an object moving in a circular path. It always points toward the center of the circle. Formula: a = v²/r, where v is the speed and r is the radius. The centripetal force required is F = mv²/r. This force is provided by tension (rope), gravity (orbit), or friction (car turning).
Acceleration and deceleration are not separate quantities — they are both acceleration with different signs. Positive acceleration means the object is speeding up (velocity increasing). Negative acceleration (deceleration or retardation) means the object is slowing down (velocity decreasing). In vector terms, when acceleration opposes the direction of motion, it decelerates the object.
To convert g-force to m/s², multiply by 9.81. Formula: m/s² = g-force × 9.81. Example: 2g = 2 × 9.81 = 19.62 m/s². To convert m/s² to g-force, divide by 9.81. Example: 30 m/s² ÷ 9.81 = 3.06g. Fighter pilots typically experience 9g during maneuvers; roller coasters generate 2–6g.
Using the free fall formula (no air resistance): s = ½ × g × t², rearranged: t = √(2s/g). Example: To fall 44.1 m on Earth: t = √(2 × 44.1 / 9.81) = √9 = 3 seconds. Use our Free Fall tab to calculate instantly for Earth, Moon, Mars and Jupiter.
All SUVAT variables must be in SI (International System) units for the equations to work correctly: s in metres (m), u and v in metres per second (m/s), a in metres per second squared (m/s²), and t in seconds (s). Our tool automatically converts km/h and mph to m/s before calculating.