Free fall calculator
m
Fall time:
No air resistance. On the graphs, velocity is positive upward, so it drops and turns negative. The blue dots beside the object mark equal time steps.
Speed at the ground:
Signed velocity (up is +):
Maximum height:
Time to maximum height:
Calculation:
This free fall calculator gives you the time an object takes to reach the ground, the speed it hits with and, if you throw it upward, the maximum height it reaches. You can drop it, throw it down or throw it up, and change the gravity to see the fall on the Moon or Mars. An animated object falls beside a height scale, and two small graphs show its position and velocity at every instant.
There is no air resistance, which is what "free fall" means in physics: only gravity acts. Below you will find the formulas, worked examples and tables.
How to use the free fall calculator
Step 1: Choose how the object starts: Dropped (initial speed 0), Thrown down or Thrown up. For the last two, enter the initial speed as a positive value.
Step 2: Enter the starting height in meters. You can use the slider. If you throw upward from the ground, the height is 0.
Step 3: Pick the gravity (Earth, Moon, Mars or custom) and click Calculate or press Enter.
Step 4: Read the fall time and the final speed. The Time control pauses the animation and shows the position and velocity at that moment.
Free fall formulas
We take upward as positive. With starting height h and initial velocity v0, the position and velocity at time t are:
| y = h + v0 × t - g × t² ÷ 2 v = v0 - g × t |
The object reaches the ground when y = 0. The speed at that moment comes from v² = v0² + 2 × g × h, and the fall time is:
| v = √(v0² + 2 × g × h) T = (v0 + v) ÷ g |
If the object is dropped (v0 = 0), you get the familiar formulas T = √(2 × h ÷ g) and v = g × T. If it is thrown upward, it rises to H = h + v0² ÷ (2 × g), takes v0 ÷ g to get there and then falls.
Gravity on Earth is 9.81 m/s² (the standard value, rounded), on the Moon 1.62 m/s² and on Mars 3.71 m/s². The mass of the object appears in none of the formulas.
Free fall examples
Example 1: An object dropped from 20 m
Dropped from 20 m on Earth, with v0 = 0:
v = √(0 + 2 × 9.81 × 20) = √392.4 ≈ 19.81 m/s
T = (0 + 19.81) ÷ 9.81 ≈ 2.019 s
It takes 2.019 s to reach the ground and hits it at 19.81 m/s, about 44.31 mph.
Example 2: A stone thrown downward
It is thrown down at 10 m/s from a 30 m bridge. Downward is negative, so v0 = -10 m/s:
v = √(100 + 2 × 9.81 × 30) = √688.6 ≈ 26.24 m/s
T = (-10 + 26.24) ÷ 9.81 ≈ 1.656 s
It reaches the water in 1.656 s at 26.24 m/s. Dropped with no speed it would have taken 2.473 s.
Example 3: A ball thrown upward
It is thrown up at 15 m/s from the ground. It rises to the height H and comes back:
H = 0 + 225 ÷ 19.62 ≈ 11.47 m
T = (15 + 15) ÷ 9.81 ≈ 3.058 s
It rises for 1.529 s, the way down takes just as long, and it touches the ground after 3.058 s at the same speed it left with, 15 m/s.
Example 4: The same fall on the Moon
Dropped from 20 m, like example 1, but with g = 1.62 m/s²:
v = √(0 + 2 × 1.62 × 20) = √64.8 ≈ 8.05 m/s
T = (0 + 8.05) ÷ 1.62 ≈ 4.969 s
The fall lasts 4.969 s, 2.46 times longer, and the impact is at only 8.05 m/s.
Fall time and speed by height
Object dropped on Earth (g = 9.81 m/s²):
| Height (m) | Fall time (s) | Final speed (m/s) | Final speed (km/h) |
|---|---|---|---|
| 1 | 0.4515 | 4.429 | 15.95 |
| 2 | 0.6386 | 6.264 | 22.55 |
| 5 | 1.01 | 9.905 | 35.66 |
| 10 | 1.428 | 14.01 | 50.43 |
| 20 | 2.019 | 19.81 | 71.31 |
| 50 | 3.193 | 31.32 | 112.76 |
| 100 | 4.515 | 44.29 | 159.46 |
Speed and distance fallen each second
Object dropped on Earth, with v = g × t and d = g × t² ÷ 2:
| Time (s) | Speed (m/s) | Distance fallen (m) |
|---|---|---|
| 1 | 9.81 | 4.905 |
| 2 | 19.62 | 19.62 |
| 3 | 29.43 | 44.15 |
| 4 | 39.24 | 78.48 |
| 5 | 49.05 | 122.63 |
Frequently asked questions
How do you calculate free fall time?
If it is dropped from a height h, T = √(2 × h ÷ g). For h = 20 m on Earth: T = √(2 × 20 ÷ 9.81) = 2.019 s.
What is the final speed of a falling object?
Use v = √(2 × g × h) when it is dropped. From 20 m it arrives at 19.81 m/s. If it has an initial speed, its square goes inside the root too.
Does mass change the fall time?
No. In free fall all objects accelerate the same, whether a feather or a rock. In real life air slows the feather more, which is why it seems to fall slower.
How far does an object fall in the first second?
It falls g × 1² ÷ 2 = 4.905 m and reaches 9.81 m/s. In the next second the speed grows another 9.81 m/s.
What about air resistance?
This calculator ignores it. In practice the speed stops growing when air drag equals the weight (terminal velocity), and for light objects or long falls the real result is lower.
Learn more
- Solved problems on free fall in physics
- Vertical projectile motion: formulas and examples
- Acceleration due to gravity in physics
- Kinematic equations for constant acceleration
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