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Free fall calculator

Give the height, the time or the landing speed and get the other two, on Earth or any planet, with the working. It leaves out air resistance.

Free fall calculator

I know the

2.02 s to fall 20 m, landing at 19.81 m/s

The ball every 0.337 s0 s0 m0.337 s0.556 m0.673 s2.22 m1.01 s5 m1.35 s8.89 m1.68 s13.9 m2.02 s20 mfallentime
Height
20 m (65.62 ft)
Time
2.02 s
Final speed
19.81 m/s (71.3 km/h, 44.3 mph)

No air resistance. A real ball, and far more so a person or a feather, falls slower than this once it's moving fast, so treat the answers as the most it could be.

Steps
  1. t = √(2h ÷ g) = √(2 × 20 ÷ 9.80665) = √4.079 = 2.02 s
  2. v = g × t = 9.80665 × 2.02 = 19.81 m/s
  3. Check: v = √(2gh) = √(2 × 9.80665 × 20) = 19.81 m/s

The same 20 m drop on each body

Bodyg (m/s²)TimeFinal speed
Sun2740.38 s104.7 m/s
Mercury3.73.29 s12.17 m/s
Venus8.872.12 s18.84 m/s
Earth9.822.02 s19.82 m/s
Moon1.624.97 s8.05 m/s
Mars3.733.27 s12.21 m/s
Jupiter*25.921.24 s32.2 m/s
Saturn*11.191.89 s21.16 m/s
Uranus*9.012.11 s18.98 m/s
Neptune*11.271.88 s21.23 m/s
Pluto0.628.03 s4.98 m/s

* No solid surface; gravity at the 1 bar level. Gravity from NASA's Planetary Fact Sheet.

Using the calculator

Pick the one you know, the height, the time or the final speed, and type it in. Heights can be in metres or feet, speeds in m/s, km/h or mph. The object starts from rest and falls straight down.

Where sets the gravity. Earth, standard g uses 9.80665 m/s², the exact value fixed for defining units. The other bodies use NASA's figures, and Other g lets you type any value. The drawing shows the ball at equal steps of time, so the gaps grow as it speeds up.

The equations

With g the acceleration from gravity, t the time, h the height fallen and v the speed at the end:

h = ½ g t², v = g t, and v = √(2 g h). Rearranged, t = √(2h ÷ g) and t = v ÷ g.

So a 20 m drop on Earth takes t = √(2 × 20 ÷ 9.80665) = 2.02 s and lands at 9.80665 × 2.02 = 19.81 m/s. On the Moon the same drop takes 4.97 s and lands at 8.05 m/s.

What about air resistance?

This calculator leaves it out, like most school physics. The equations are exact in a vacuum, and close for a dense object over a short drop. Over a long drop, air pushes back harder as the object speeds up, until it stops gaining speed at all. A real fall is slower than these answers, so treat them as the most it could be.

On the Moon there's no air to speak of, so the answers there are what you'd see.

Questions

How long does it take to fall 20 metres?

2.02 seconds on Earth with no air resistance, landing at 19.81 m/s (71.3 km/h).

How far does something fall in 3 seconds?

44.13 m, and it's going 29.42 m/s by then, using g = 9.80665 m/s².

Do heavy things fall faster than light things?

Not without air. Every object falls with the same acceleration g, whatever its mass. With air, a light, spread-out object like a feather is slowed far more than a stone.

What value of g should I use?

9.81 m/s² is the usual school figure, and 9.80665 m/s² is the standard value. Real gravity varies a little from place to place on Earth.

How long does a fall take on Mars?

Mars's gravity is 3.73 m/s², so a 20 m drop takes 3.27 s and lands at 12.21 m/s.

What does free fall mean?

Moving under gravity alone, with no other force acting. Here the object also starts from rest and falls straight down.

Sources

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