Acceleration Calculator

Acceleration is the rate at which an object’s velocity changes over time. Newton’s Second Law of Motion connects acceleration, force and mass, and it is one of the most useful equations in all of physics.

Newton’s Second Law: F = m × a Which rearranges to: a = F ÷ m (acceleration equals net force divided by mass) m = F ÷ a (mass equals force divided by acceleration)

Kinematic acceleration formula: a = (v_f − v_i) ÷ t where v_f = final velocity, v_i = initial velocity, t = time elapsed.

Units:

• Force (F) in Newtons (N) = kg·m/s²
• Mass (m) in kilograms (kg)
• Acceleration (a) in meters per second squared (m/s²)
• In imperial: Force in pounds-force (lbf), mass in slugs, acceleration in ft/s²

Key reference accelerations:

• Earth’s gravity (g) = 9.81 m/s² (32.2 ft/s²)
• Typical car 0–60 mph (0–97 km/h) = ~5–8 m/s² for performance cars
• Space Shuttle ≈ 5 m/s² at liftoff, rising to a capped 29 m/s² (3g) late in the ascent as the tanks empty
• Fighter jet maximum ≈ 88 m/s² (~9g) in a tight turn
• Bullet from rifle ≈ 1,000,000 m/s² in barrel (extremely brief)
• Human unconsciousness threshold ≈ 50–100 m/s² sustained (5–10g)

Worked example 1, Newton’s Second Law (use the acceleration from force calculator for this one): A 1,200 kg car engine applies 4,800 N of net force. a = F ÷ m = 4,800 ÷ 1,200 = 4 m/s² From rest (v_i = 0), after 5 seconds: v_f = 0 + 4 × 5 = 20 m/s (72 km/h or 45 mph)

Worked example 2, the kinematic case this page solves: A ball rolling at 2 m/s decelerates to a stop in 4 seconds. a = (0 − 2) ÷ 4 = −0.5 m/s² (deceleration / negative acceleration) Braking force on a 0.5 kg ball = 0.5 × 0.5 = 0.25 N

Gravity on other planets (m/s²):

• Moon: 1.62 | Mars: 3.72 | Venus: 8.87 | Jupiter: 24.8 | Saturn: 10.4

The same force applied to a smaller mass produces greater acceleration, which is why a baseball bat accelerates faster than a car when pushed with the same force.