Free Fall Calculator: Fall Time, Impact Speed and Projectile Motion
How this free fall calculator works: dropped from height h, an object needs t = √(2h/g) seconds without air resistance and hits the ground at v = √(2gh). From 20 m that is 2.02 s and 19.8 m/s (44 mph). Pick a mode below – you get the working and a time table of the motion.
Example: What do you know: Drop height → fall time and velocity · Drop height h 20 m · Planet or moon: Earth (9.806 65 m/s²) → Result: Fall time 2.02 s · impact at 19.81 m/s (71.3 km/h). Source: CODATA, NIST CODATA – standard acceleration of gravity g_n = 9.806 65 m/s² (exact). Updated: .
How it is calculated
Free fall equations
In free fall an object starts at rest and accelerates uniformly at g. On Earth the standard value is g = 9.806 65 m/s² (exact by definition, NIST/CODATA); the local value ranges from about 9.78 m/s² at the equator to 9.83 m/s² at the poles.
- Distance fallen: h = ½ · g · t²
- Fall time: t = √(2h / g)
- Velocity: v = g · t = √(2 · g · h)
Mass appears nowhere: without air, a hammer and a feather fall together – Apollo 15 astronaut David Scott showed exactly that on the Moon in 1971.
Example: a 20 m drop
- t = √(2 · 20 m / 9.806 65 m/s²) = √4.079 s² ≈ 2.02 s
- v = 9.806 65 m/s² · 2.02 s ≈ 19.8 m/s = 71.3 km/h (44.3 mph)
Rule of thumb: after 1 s an object has fallen about 4.9 m (16 ft), after 2 s 19.6 m, after 3 s 44.1 m – distance grows with the square of time.
Projectile motion
A launch speed v₀ at angle α splits into a horizontal part vₓ = v₀ · cos α, which stays constant, and a vertical part v_y = v₀ · sin α, which gravity slows down. The path is a parabola:
- Range on level ground: R = v₀² · sin(2α) / g – largest at 45°
- Maximum height: h_max = h₀ + (v₀ · sin α)² / (2g)
- Horizontal launch (α = 0°) from height h₀: flight time √(2h₀/g), range v₀ · √(2h₀/g)
With a launch height the calculator uses the general time of flight T = (v_y + √(v_y² + 2 g h₀)) / g. Example: 20 m/s at 45° from the ground travels 40.8 m and peaks at 10.2 m.
Limitations
Air resistance is ignored. That is a good approximation for dense, compact objects over short distances; for high speeds, light objects or skydiving the real velocity is much lower. Values for other bodies come from NASA’s Planetary Fact Sheet.
More physics: the stopping distance calculator covers braking cars, and the scientific notation converter handles very large or small numbers.
Frequently asked questions
How do you calculate free fall time?
Use t = √(2h / g). From 10 m: t = √(2 · 10 / 9.81) ≈ 1.43 s. Air resistance is ignored.
How do you find the velocity of a falling object?
v = g · t if you know the time, or v = √(2 · g · h) from the height. A 20 m drop gives √(2 · 9.81 · 20) ≈ 19.8 m/s, about 44 mph.
How far does an object fall in a given time?
h = ½ · g · t². A stone dropped into a well for 3 s falls ½ · 9.81 · 9 ≈ 44 m (ignoring the time the sound needs to come back up).
Do heavier objects fall faster?
Not in a vacuum: mass cancels out of the equations. In air, light and wide objects fall more slowly because drag is large compared with their weight.
What is the range of a projectile launched at 45°?
On level ground R = v₀² / g. At 20 m/s that is 400 / 9.81 ≈ 40.8 m. Without drag, 45° gives the maximum range; from a raised launch point the best angle is slightly lower.
Does this free fall calculator include air resistance?
No. Drag would need air density, cross-section and a drag coefficient. The results are therefore upper limits for speed and range.
Sources and legal basis
- CODATA: NIST CODATA – standard acceleration of gravity g_n = 9.806 65 m/s² (exact)
- NASA NSSDC: NASA NSSDC – Planetary Fact Sheet (Metric), row “Gravity (m/s²)”
- OpenStax: OpenStax University Physics Vol. 1, 3.5 Free Fall and 4.3 Projectile Motion
As of:
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