What this calculator does
Find out how long a fall takes and how fast something is going when it lands. An object in free fall is pulled by gravity alone. Without air resistance, every object near the ground speeds up by the same amount each second. Its weight doesn't matter. On Earth it goes about 9.81 m/s (meters per second) faster every second. So you can predict the fall from just the drop height and the gravity.
Enter the height, and the calculator shows how long the fall takes and the speed at landing. A table tracks the position and speed all the way down. You can add a starting speed for something thrown straight down. You can pick the Moon or Mars, too. And you can ask where the object is at a particular time.
Where it's used
Why this math matters outside the classroom:
- Dropped stone. A stone dropped from 20 m hits the ground after √(2 × 20 ÷ 9.81), about 2 seconds, at roughly 19.8 m/s.
- Well depth. Hikers estimate a well's depth by timing a dropped pebble: 3 seconds of fall means about 44 m, ignoring sound travel time.
- Drop towers. Amusement-park drop towers give riders a few seconds of near free fall before brakes slow the car.
- Site safety. Construction safety trainers show that a tool dropped from 45 m reaches about 30 m/s, the reason behind hard-hat rules.
- Galileo's idea. Classes test Galileo's idea that, without air resistance, a heavy ball and a light ball fall at the same rate.
Grade level and standards: Grades 9–10; Common Core State Standards for Mathematics HSA.REI.B.4.b. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
How to use it
- Enter the drop height, measured from the release point to the ground.
- Leave the initial velocity at 0 for a simple drop, or enter the speed of a downward throw.
- Choose the gravity: Earth, Moon, Mars or a custom value such as 9.8 m/s².
- If you like, enter a time to see the distance fallen and the speed at that moment. Then read the results, the working and the table.
What the inputs mean
- Drop height (h)
- Vertical distance from the release point down to the ground.
- Initial downward velocity (u)
- Only downward throws are handled here. For something thrown upward or at an angle, use the projectile motion calculator.
- Custom gravitational acceleration
- Textbooks often use 9.8 m/s², 9.81 m/s², 10 m/s² or 32 ft/s². Enter the one your problem uses, so your answers match.
- Check position after time (t)
- Leave it blank if you only need the fall time and impact speed. A time after landing shows the object resting on the ground.
Formula and method
v = √(u² + 2 × g × h) t = 2h ÷ (u + v) (same as (v − u) ÷ g) d(t) = u × t + ½ × g × t² v(t) = u + g × t
In the formulas, h is the drop height and g is the pull of gravity. u is the starting downward speed, and v is the speed when it lands. t is the time, and d(t) and v(t) are the distance fallen and speed after time t.
The landing speed comes from a standard formula for steady speeding up: v² = u² + 2gh. For a simple drop (u = 0), it becomes v = √(2gh). The fall time becomes t = √(2h ÷ g).
The fall time is the height divided by the average speed. When something speeds up steadily, its average speed is exactly halfway between start and end: (u + v) ÷ 2. That gives t = 2h ÷ (u + v). It's the same as (v − u) ÷ g, but it stays accurate even when the throw speed is large.
Worked example
A stone is dropped from rest off a 20 m bridge on Earth. How long does it take to reach the water, and how fast is it going?
- Impact speed: v = √(0² + 2 × 9.80665 × 20) = 19.805706 m/s.
- Fall time: t = (2 × 20) ÷ (0 + 19.805706) = 2.01962 s.
- After 1 s it has fallen 0.5 × 9.80665 × 1² = 4.903325 m and is moving at 9.80665 m/s.
Result: The stone hits the water after about 2.02 s, going about 19.81 m/s (roughly 71.3 km/h). After the first second, it's still 15.096675 m above the water.
Understanding the result
Fall time grows with the square root of the height. So four times the height takes only twice as long. Landing speed grows the same way, so a drop 4× higher doubles the landing speed.
Mass cancels out of the math. So in a vacuum, a heavy object and a light one dropped together land together. In air, light or broad objects fall noticeably slower. Treat the results as the fastest the object could go.
Assumptions and limitations
- No air resistance (drag) at all.
- Gravity stays the same over the whole fall. That's accurate for heights that are small compared with the size of the planet.
- The ground is flat and the object moves straight down.
- Real objects in air reach a terminal velocity, a top speed where air pushes back as hard as gravity pulls. For long drops or light objects, the real speed is much lower than shown here.
- Very large heights (tens of kilometers and up) need gravity that weakens as you go higher.
- Upward or angled throws aren't covered. Use the projectile motion calculator for those.
Frequently asked questions
Do heavier objects fall faster?
Not without air resistance. Gravity speeds up every object by the same amount, so in a vacuum a feather and a hammer fall together. In air, drag (air pushing back) slows light, broad objects more. That's why they seem to fall more slowly.
How long does it take to fall 100 m?
Without air resistance on Earth, t = √(2 × 100 ÷ 9.80665) ≈ 4.52 s. It would reach about 44.3 m/s. With real air resistance, a person or object would be somewhat slower.
What value of g does the calculator use?
By default, it uses the standard value, 9.80665 m/s². You can choose the Moon (1.62 m/s²) or Mars (3.71 m/s²). Or enter your own value, such as 9.8 m/s², to match your textbook.
What if the time I enter is after the object lands?
The calculator shows that it has fallen the full height and is on the ground. The formulas stop applying once it hits something.
How this calculator is checked
Method: Constant-acceleration kinematics: v² = u² + 2gh, d = ut + ½gt², v = u + gt; fall time from t = 2h ÷ (u + v). The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.
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