Free-fall gravity calculator
Enter the height you drop an object from and the time it takes to hit the floor. The calculator gives you the acceleration due to gravity and compares it with Earth, the Moon and Jupiter.
Key formula
d = ½ · g · t² · g = 2d / t²
Try it
How to use the simulator
This calculator recreates the simplest way to measure gravity: drop an object from a known height and time how long it takes to hit the floor. Since it starts at rest, the distance covered is d = ½·a·t², which rearranges to a = 2d / t². The bar compares your result with Earth, the Moon, Jupiter and the gravity Grace measures on board.
Controls
- Drop height (m): how far the object falls.
- Fall time (s): what the stopwatch reads at impact.
Things to try
- Enter Grace's numbers (0.91 m and 0.348 s) and check that you get about 15 m/s², roughly 1.5 times Earth's gravity.
- Keep the height at 0.91 m and find the time that gives 9.8 m/s² (about 0.43 s). It differs from 0.348 s by less than a tenth of a second, which is why a reliable timer matters.
- Nudge the time by just 0.01 s and watch the result move. Because time is squared, small timing errors have a big effect.
Loading simulator…
Free fall
If you release an object from rest and air barely slows it, its speed increases steadily: every second it gains the same amount of speed, which is exactly the acceleration due to gravity, g. The distance covered grows with the square of the time.
Rearranging d = ½·g·t² gives g = 2d/t². All you need is a tape measure and a stopwatch. At Earth's surface the answer is about 9.81 m/s², with small variations by latitude and altitude.
The stopwatch problem
Because time is squared, any timing error is amplified: a 3% error in time gives a 6% error in gravity. A one-meter fall lasts under half a second, about the same as human reaction time, so with a handheld stopwatch the result isn't very reliable.
That is why labs use optical sensors, or prefer a pendulum, which lets you time many swings in a row and spread the error. Modern gravimeters drop a mirror inside a vacuum chamber and track it with a laser, to one part in a billion.
Worked example
Example: dropping a ball from 2 meters
- Drop a ball from 2 m and suppose it takes 0.639 s to reach the floor.
- g = 2 · 2 / 0.639² = 4 / 0.408 ≈ 9.80 m/s², Earth's gravity.
- If you are off by just 0.02 s and read 0.619 s, you get g ≈ 10.4 m/s²: 6% more from a three-hundredths error.
- With 0.91 m and 0.348 s (the novel's numbers) you get about 15 m/s², 1.5 times Earth's gravity.
In Project Hail Mary
The novel's main character drops objects and times the fall to find out whether the gravity he feels is Earth's. It turns out to be clearly stronger, which gives him the first clue to where he is.
Frequently asked questions
Do a feather and a hammer fall at the same rate?
In a vacuum, yes. Astronaut David Scott showed it on the Moon in 1971 during Apollo 15. On Earth the feather falls slower only because of air resistance.
Is gravity the same all over Earth?
Not quite. It is slightly stronger at the poles (about 9.83 m/s²) than at the equator (about 9.78 m/s²), because of Earth's rotation and its slightly flattened shape. It also decreases with altitude.
What is gravity on other planets?
On the Moon, 1.62 m/s²; on Mars, 3.71; on Jupiter, at cloud-top level, about 24.8 m/s².