Acceleration Calculator
Calculate acceleration, velocity, or time from kinematic data. Enter any three values to solve for the fourth — includes Newton's Second Law and displacement calculations.
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Enter your values above to see the results.
Tips & Notes
- ✓Acceleration is a vector — direction matters. Deceleration is negative acceleration: a car braking from 30 m/s to 0 in 5 s has a = (0−30)/5 = −6 m/s², not +6 m/s².
- ✓The SI unit is m/s² (meters per second squared). In automotive contexts, acceleration is often expressed in g-forces: 1g = 9.81 m/s². A 0-60 mph (0-26.8 m/s) car in 4 seconds produces 6.7 m/s² = 0.68g.
- ✓For free fall (no air resistance), all objects accelerate at g = 9.81 m/s² regardless of mass. A 1 kg ball and a 100 kg ball dropped from the same height hit the ground at the same time.
- ✓Average acceleration uses start and end velocities. For non-constant acceleration, you need the area under a velocity-time graph (integration) — this calculator computes average acceleration only.
- ✓Use Newton's Second Law (F = ma) to find the force producing an acceleration: if a 1,200 kg car accelerates at 3 m/s², the net force required is F = 1,200 × 3 = 3,600 N.
Common Mistakes
- ✗Confusing speed and velocity — speed is scalar (magnitude only), velocity is vector (magnitude and direction). Acceleration is the rate of change of velocity, so direction changes also produce acceleration even at constant speed (circular motion).
- ✗Forgetting to convert units before calculating — mixing km/h with m/s gives wrong results. Convert: 1 km/h = 0.2778 m/s. A car going from 0 to 100 km/h (27.78 m/s) in 5 s: a = 27.78/5 = 5.56 m/s², not 100/5 = 20.
- ✗Treating deceleration as positive — a braking vehicle has negative acceleration (in the direction of motion). If the problem asks for the magnitude only, take the absolute value after calculating.
- ✗Using average acceleration for non-linear motion — this formula gives average acceleration between two points. If the acceleration varies (e.g., a car with changing throttle), the result is only the average, not instantaneous values.
- ✗Ignoring the sign when combining accelerations — if a rocket accelerates upward at 15 m/s² but gravity pulls down at 9.81 m/s², the net upward acceleration is 15 − 9.81 = 5.19 m/s², not 15 + 9.81.
Acceleration Calculator Overview
Acceleration is the fundamental kinematic quantity connecting force, mass, and motion — it appears in every mechanics problem from projectile motion to rocket propulsion. Understanding how to calculate and interpret acceleration is the foundation of classical physics and mechanical engineering.
Average acceleration formula:
a = (v_f − v_i) / t | Units: m/s² (SI), ft/s² (imperial)
EX: Vehicle accelerates from 0 to 27.8 m/s (100 km/h) in 5.0 s → a = (27.8 − 0) / 5.0 = 5.56 m/s² = 0.567g. Braking from 27.8 m/s to 0 in 3.0 s → a = (0 − 27.8) / 3.0 = −9.27 m/s² = −0.945g (deceleration)Newton's Second Law — force and acceleration:
F = m × a | a = F / m | Units: N = kg·m/s²
EX: 1,200 kg car, net driving force 3,600 N → a = 3,600 / 1,200 = 3.0 m/s². Same car braking with 8,400 N stopping force → a = −8,400 / 1,200 = −7.0 m/s²Kinematic reference — acceleration, velocity, and distance:
| Known Variables | Find | Equation | Example |
|---|---|---|---|
| v_i, v_f, t | a | a = (v_f − v_i) / t | 0→30 m/s in 6s: a = 5 m/s² |
| v_i, a, t | v_f | v_f = v_i + a×t | v_i=10, a=3, t=4: v_f=22 m/s |
| v_i, a, t | d | d = v_i×t + ½a×t² | 0 m/s, 5 m/s², 4s: d=40 m |
| v_i, v_f, a | d | d = (v_f²−v_i²) / (2a) | 0→20 m/s at 4 m/s²: d=50 m |
| F, m | a | a = F / m | 4500 N, 1500 kg: a=3 m/s² |
| Scenario | Acceleration | G-Force |
|---|---|---|
| Gravity (free fall) | 9.81 m/s² | 1.0g |
| Comfortable elevator | 1–2 m/s² | 0.1–0.2g |
| Typical car (0–100 km/h in 8s) | 3.5 m/s² | 0.35g |
| Sports car (0–100 km/h in 4s) | 6.9 m/s² | 0.70g |
| Emergency braking (dry road) | 8–10 m/s² | 0.8–1.0g |
| Fighter jet (sustained) | 49–69 m/s² | 5–7g |
| Rocket launch (Apollo) | ~29 m/s² | ~3g |
Frequently Asked Questions
Use the formula a = (v_f − v_i) / t, where v_f is final velocity, v_i is initial velocity, and t is time elapsed. Example: a car accelerates from 10 m/s to 30 m/s in 4 seconds → a = (30 − 10) / 4 = 20 / 4 = 5 m/s². If the car had started from rest (v_i = 0), the calculation simplifies to a = v_f / t. Always subtract initial from final velocity — the order matters for getting the correct sign.
Deceleration is simply negative acceleration — the same equation applies, but the result is negative when an object slows down. If a car brakes from 25 m/s to 5 m/s in 4 seconds: a = (5 − 25) / 4 = −5 m/s². The negative sign indicates deceleration. In physics, we avoid the word "deceleration" and use "negative acceleration" because it is more precise — an object can decelerate in one direction while accelerating in another (circular motion).
Newton's Second Law states F = m × a, or equivalently a = F / m. A net force applied to a mass produces acceleration proportional to the force and inversely proportional to the mass. Example: a 1,500 kg car with a net driving force of 4,500 N (after subtracting friction and drag) accelerates at a = 4,500 / 1,500 = 3 m/s². Doubling the force doubles the acceleration; doubling the mass halves the acceleration.
Gravitational acceleration g = 9.81 m/s² (9.807 m/s² precisely) is the acceleration any object experiences in free fall near Earth's surface in a vacuum. It acts downward. For projectile problems: vertical acceleration = −9.81 m/s² (downward), horizontal acceleration = 0 (no horizontal force in vacuum). Example: a ball dropped from rest reaches v_f = g × t after t seconds. After 3 seconds: v_f = 9.81 × 3 = 29.43 m/s downward.
Use the kinematic equation: d = v_i × t + ½ × a × t². Example: a car starts from rest (v_i = 0) and accelerates at 4 m/s² for 6 seconds → d = 0 × 6 + ½ × 4 × 6² = 0 + 2 × 36 = 72 meters. Alternatively, use d = (v_i + v_f) / 2 × t when you know both velocities: average velocity = (0 + 24) / 2 = 12 m/s, distance = 12 × 6 = 72 m. Both equations give the same result for constant acceleration.
One g-force equals the standard gravitational acceleration: 1g = 9.81 m/s². G-force is used in aviation, automotive testing, and roller coasters. Convert: acceleration in g = a (m/s²) / 9.81. A fighter jet accelerating at 49 m/s² experiences 49 / 9.81 = 5g. Humans can typically withstand 4-6g sustained; astronauts during launch experience 3g; a typical sports car does 0-60 mph in about 0.5g. Above 9g, unconsciousness typically occurs within seconds.