Acceleration Calculator
Calculate acceleration from velocity change and time, or from force and mass. Find initial/final velocity, time, and distance with kinematic equations.
Acceleration
4.0000 m/s²
In g-force
0.4079 g
In ft/s²
13.1234 ft/s²
Type
Acceleration
Calculation
a = (v - v₀) / t
a = (20.00 - 0.00) / 5
= 4.0000 m/s²
G-Force Reference
- • 1 g = 9.81 m/s² (Earth gravity)
- • Car braking: 0.3-0.8 g
- • Roller coaster: 3-5 g
- • Fighter jet: up to 9 g
- • Space launch: 3-4 g
Related Calculators
About This Calculator
Acceleration is the rate at which velocity changes over time. Whether a car speeds up, a ball falls, or a rocket launches, acceleration describes how quickly the motion changes. This calculator helps you find acceleration using multiple methods: from velocity change, from force and mass, or from distance traveled.
What is Acceleration? Acceleration measures how quickly velocity changes. Positive acceleration means speeding up in the direction of motion; negative acceleration (deceleration) means slowing down. The SI unit is meters per second squared (m/s²).
Key Formulas:
- a = Δv / t (velocity change over time)
- a = F / m (Newton's Second Law)
- a = 2(d - v₀t) / t² (from distance and time)
- v² = v₀² + 2ad (velocity-acceleration-distance)
Why Acceleration Matters:
- Vehicle safety and performance design
- Physics problem-solving
- Sports science and training
- Aerospace engineering
- Amusement ride safety
This calculator handles multiple acceleration scenarios. For related physics, see our Velocity Calculator and Force Calculator.
How to Use the Acceleration Calculator
- 1Select your calculation method based on known values.
- 2For velocity-time: Enter initial velocity, final velocity, and time.
- 3For force-mass: Enter net force and mass.
- 4For distance-time: Enter initial velocity, distance, and time.
- 5Choose velocity units (m/s, km/h, or mph).
- 6Review the calculated acceleration in m/s².
- 7Check the g-force equivalent for physical context.
- 8Negative values indicate deceleration.
- 9Compare with reference values for real-world context.
- 10Use the appropriate formula for your problem.
Acceleration Formulas
Multiple ways to calculate acceleration.
From Velocity and Time
a = (v - v₀) / t
The most common formula. Measures rate of velocity change.
Example: Car accelerates from 0 to 27 m/s in 6 seconds a = (27 - 0) / 6 = 4.5 m/s²
From Force and Mass (Newton's Second Law)
a = F / m
Relates acceleration to the cause (force) and resistance (mass).
Example: 1000 N force on 200 kg object a = 1000 / 200 = 5 m/s²
From Distance and Time
a = 2(d - v₀t) / t²
Derived from d = v₀t + ½at². Useful when you know distance traveled.
Example: Starting at rest, travels 100 m in 10 s a = 2(100 - 0) / 100 = 2 m/s²
From Velocity and Distance
a = (v² - v₀²) / 2d
When you don't know time.
Example: Accelerates from 10 to 30 m/s over 200 m a = (900 - 100) / 400 = 2 m/s²
Understanding G-Force
Relating acceleration to gravitational force.
What is G-Force?
G-force expresses acceleration relative to Earth's gravity: 1 g = 9.80665 m/s²
It's not actually a force, but a convenient way to express acceleration.
Converting
g-force = acceleration / 9.80665 acceleration = g-force × 9.80665
Human Tolerance
| G-Force | Effect |
|---|---|
| 1 g | Normal (standing on Earth) |
| 2-3 g | Noticeable pressure, breathing harder |
| 4-6 g | Difficulty moving, vision narrowing |
| 7-9 g | Consciousness affected, risk of blackout |
| > 10 g | Risk of injury, unconsciousness |
Real-World G-Forces
| Activity | Approximate G |
|---|---|
| Walking | 1.0-1.2 g |
| Car braking hard | 0.7-1.0 g |
| Roller coaster | 3-5 g |
| Formula 1 cornering | 4-6 g |
| Fighter jet | up to 9 g |
| Space shuttle launch | 3 g |
| Bullet fired | 100,000+ g |
Duration Matters
High g-forces are survivable for very short times. The same g-force sustained for seconds becomes dangerous.
Acceleration vs. Deceleration
Understanding positive and negative acceleration.
Signs and Direction
Acceleration is a vector - it has direction.
Positive acceleration:
- Object speeding up in the positive direction
- Object slowing down in the negative direction
Negative acceleration:
- Object slowing down in the positive direction
- Object speeding up in the negative direction
Common Convention
- Define direction of initial motion as positive
- Speeding up → acceleration in same direction as motion
- Slowing down → acceleration opposite to motion
Examples
Car accelerating forward:
- v₀ = 10 m/s, v = 20 m/s
- a = +2 m/s² (positive, speeding up)
Car braking:
- v₀ = 20 m/s, v = 10 m/s
- a = -2 m/s² (negative, slowing down)
Thrown ball going up:
- v₀ = +20 m/s (up), a = -9.8 m/s² (gravity down)
- Ball slows while rising
Ball falling down:
- v₀ = 0, a = -9.8 m/s²
- Ball speeds up while falling (velocity becomes more negative)
Constant vs. Variable Acceleration
When acceleration changes over time.
Constant Acceleration
All kinematic equations assume constant acceleration:
- v = v₀ + at
- d = v₀t + ½at²
- v² = v₀² + 2ad
- d = ½(v₀ + v)t
Examples:
- Free fall (ignoring air resistance)
- Uniform braking
- Idealized vehicle acceleration
Variable Acceleration
Real-world acceleration often changes:
- Car accelerating: a decreases as speed increases
- Rocket: a increases as fuel burns (less mass)
- Falling with air resistance: a decreases as drag increases
Handling Variable Acceleration
For variable acceleration:
- Use calculus: a = dv/dt
- Average acceleration: ā = Δv / Δt
- Numerical integration
- Approximate as piecewise constant
Average Acceleration
ā = (v_final - v_initial) / (t_final - t_initial)
Gives the constant acceleration that would produce the same velocity change.
Practical Applications
Real-world acceleration calculations.
Vehicle Performance
0-60 mph (0-26.8 m/s) in 5 seconds: a = 26.8 / 5 = 5.36 m/s² ≈ 0.55 g
Braking from 100 km/h (27.8 m/s) in 50 m: a = -(27.8)² / (2 × 50) = -7.7 m/s² ≈ 0.79 g
Sports Science
Sprint start (0 to 10 m/s in 1.5 s): a = 10 / 1.5 = 6.67 m/s² ≈ 0.68 g
Baseball pitch deceleration in catcher's mitt: ~40 m/s to 0 in 0.01 s = 4000 m/s² ≈ 408 g
Engineering
Elevator acceleration (comfortable): Target: < 1.5 m/s² (0.15 g)
Crash testing: Survivable: < 60 g for short duration
Aerospace
Rocket launch acceleration: Typical: 20-40 m/s² (2-4 g)
Orbital velocity change: To reach orbit: need ~8 km/s velocity Achieved over minutes at sustainable g-force
Centripetal Acceleration
Acceleration in circular motion.
What is Centripetal Acceleration?
Objects moving in circles are constantly accelerating toward the center, even at constant speed. This is centripetal ("center-seeking") acceleration.
Formula
a_c = v² / r = ω²r
Where:
- v = tangential velocity
- r = radius of circular path
- ω = angular velocity (rad/s)
Examples
Car on circular track: v = 30 m/s, r = 100 m a_c = 900 / 100 = 9 m/s² ≈ 0.92 g
Earth's orbit around Sun: v ≈ 30,000 m/s, r ≈ 150 billion m a_c ≈ 0.006 m/s² (very small!)
Centrifuge: ω = 10,000 rpm = 1047 rad/s, r = 0.1 m a_c = 1047² × 0.1 = 109,600 m/s² ≈ 11,000 g
Why You Feel It
In a turning car, your body wants to continue straight (inertia). The car pushes you toward the center, creating the sensation of being pushed outward (centrifugal "force" - actually just inertia).
Pro Tips
- 💡Acceleration can be positive or negative - it indicates direction, not just magnitude.
- 💡Use a = Δv/t for constant acceleration problems.
- 💡Newton's Second Law (a = F/m) connects force to acceleration.
- 💡1 g = 9.81 m/s² - use this to convert to g-force.
- 💡Deceleration is just negative acceleration (opposite to motion direction).
- 💡Check units: velocity in m/s, time in s, gives acceleration in m/s².
- 💡For variable acceleration, calculus or numerical methods are needed.
- 💡Centripetal acceleration = v²/r for circular motion.
- 💡Average acceleration doesn't tell you about instantaneous values.
- 💡High g-forces are survivable briefly but dangerous if sustained.
- 💡Zero velocity doesn't mean zero acceleration.
- 💡Direction conventions: usually positive = direction of initial motion.
Frequently Asked Questions
Velocity measures how fast and in what direction you're moving (m/s). Acceleration measures how quickly your velocity is changing (m/s²). You can have high velocity with zero acceleration (constant speed) or high acceleration with zero velocity (starting from rest).
