Gravity / Free Fall Calculator
Calculate free fall time and impact velocity from height, or find height from fall time.
Supports both metric and imperial units.
Gravity is the fundamental force that attracts any two objects with mass toward each other. Sir Isaac Newton formulated the law of universal gravitation in 1687, and it remains one of the most important equations in all of physics.
Newton’s Law of Universal Gravitation:
F = G × (m₁ × m₂) / r²
Free-fall acceleration (near Earth’s surface):
d = ½ × g × t²
v = g × t
What each variable means:
- F — gravitational force between the two objects (Newtons, N)
- G — gravitational constant = 6.674 × 10⁻¹¹ N·m²/kg²
- m₁, m₂ — masses of the two objects (kilograms)
- r — distance between their centers (meters)
- g — gravitational acceleration on Earth’s surface = 9.81 m/s²
- d — distance fallen (meters)
- t — time of free fall (seconds)
- v — velocity at time t (m/s)
Worked example — free fall: An object is dropped from a 50-meter building. How long does it take to hit the ground, and how fast is it moving at impact?
d = ½ × g × t² → 50 = ½ × 9.81 × t² → t² = 10.19 → t = 3.19 seconds v = g × t = 9.81 × 3.19 = 31.3 m/s (≈ 113 km/h)
Worked example — gravitational force: Force between Earth (5.97 × 10²⁴ kg) and a 70 kg person standing on the surface (r = 6.371 × 10⁶ m): F = 6.674 × 10⁻¹¹ × (5.97 × 10²⁴ × 70) / (6.371 × 10⁶)² F ≈ 686 N — which matches weight = mg = 70 × 9.81 = 686.7 N ✓
Reference values by planet (surface g):
- Moon: 1.62 m/s² | Mars: 3.72 m/s² | Earth: 9.81 m/s² | Jupiter: 24.8 m/s²
Air resistance is ignored in free-fall calculations. Real objects reach a terminal velocity when air drag equals gravitational force (e.g., ~195 km/h for a skydiver in a stable freefall position).