Kinematics Calculator (Uniform Motion, Acceleration, Free Fall, Projectile)

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free fall calculator

Free fall calculator: time, height and impact speed

In free fall only gravity acts and the acceleration is a constant g. Any two of height, time and final speed fix the third. Enter what you know, choose the value of g and read the result.

The free-fall formulas and what changes with g

Starting from rest, the distance fallen is h = g·t²/2, the speed is v = g·t and, without time, v² = 2·g·h. Solving, t = √(2h/g) and v = √(2·g·h). Mass does not appear: in a vacuum a bowling ball and a feather land together. A 45 m fall with g = 10 m/s² takes 3 s and ends at 30 m/s, which is 108 km/h. A 100 m fall with g = 9.80665 m/s² takes about 4.52 s and ends at about 44.3 m/s, or 159 km/h.
The value of g depends on the problem. 10 m/s² makes exercises easy, 9.8 m/s² is the usual school value and 9.80665 m/s² is standard gravity, exact by definition. On other bodies it changes a lot: 1.62 m/s² on the Moon and 3.73 m/s² on Mars (NASA fact sheets). A 10 m fall lasts 1.43 s on Earth with 9.80665, 2.32 s on Mars and 3.51 s on the Moon, arriving at 14.0, 8.64 and 5.69 m/s respectively.
If the object is thrown down rather than dropped, an initial speed enters: h = v₀·t + g·t²/2. Throwing a stone downward at 10 m/s from 15 m with g = 10 m/s² gives 5t² + 10t - 15 = 0, whose positive root is t = 1 s, and the stone arrives at 20 m/s. A neat pattern for motion from rest: in successive seconds the object covers distances in the ratio 1 : 3 : 5 : 7, that is 5 m, 15 m, 25 m and 35 m with g = 10 m/s².
The model ignores air. For short falls of dense objects the error is small, but for paper, leaves or skydivers drag grows with speed until it balances the weight, and the speed approaches a terminal value instead of growing without limit. The calculator gives the ideal case, which is what school exercises and most exams ask for.

Six falls worked out

45 m fall (g = 10)

Input: h = 45 m, g = 10 m/s²
Expected output: t = 3 s, v = 30 m/s

t = √(2·45/10) = 3 and v = 10·3.

100 m fall with standard g

Input: h = 100 m, g = 9,80665 m/s²
Expected output: t ≈ 4,52 s, v ≈ 44,3 m/s (159 km/h)

v = √(2·9.80665·100) = 44.29 m/s, times 3.6.

Height from the time

Input: t = 4 s, g = 10 m/s²
Expected output: h = 80 m, v = 40 m/s

h = 10·16/2 = 80.

10 m fall on the Moon

Input: h = 10 m, g = 1,62 m/s²
Expected output: t ≈ 3,51 s, v ≈ 5,69 m/s

A fall that lasts 1.43 s on Earth.

10 m fall on Mars

Input: h = 10 m, g = 3,73 m/s²
Expected output: t ≈ 2,32 s, v ≈ 8,64 m/s

Between Earth and the Moon.

Thrown downward

Input: v₀ = 10 m/s, h = 15 m, g = 10 m/s²
Expected output: t = 1 s, v = 20 m/s

The root t = -3 s of the quadratic is discarded.

Full tool FAQ

What is the difference between uniform motion and constant acceleration?

In uniform motion the velocity does not change (zero acceleration) and position grows along a straight line on the s-t graph: S = S₀ + v·t. With constant acceleration the acceleration is non-zero, velocity changes linearly, v = v₀ + a·t, and the s-t graph is a parabola: S = S₀ + v₀·t + a·t²/2. Uniform motion is the special case with a = 0. A car at a steady 72 km/h covers 100 m in 5 s; one starting from rest with a = 2 m/s² covers 25 m in the same 5 s.

How do I convert km/h to m/s?

When should I use Torricelli's equation?

Which g should I use: 9.8, 10 or 9.80665?

How long does a free fall take and how fast does the object arrive?

How do I find the range and maximum height of an oblique launch?

Why do two different angles give the same range?

Why is average speed not the mean of the speeds?

What do two solutions or the negative time warning mean?

Does the calculator include air resistance?

Frequently asked questions

Does a heavier object fall faster?

In a vacuum, no: the acceleration is g for any mass and both land together. In air, the object with larger area and lower density feels more drag and takes longer, which explains the feather and the stone. The calculator uses a vacuum.

How can I find the depth of a well by timing a drop?

Drop a stone and time it until you hear the splash. With 2 s of fall and g = 10 m/s², h = 10·4/2 = 20 m. In deep wells the sound takes time to come back up (about 340 m/s) and that delay must be subtracted from the measured time.

Is gravity the same everywhere on Earth?

Not exactly. It ranges from about 9.78 m/s² at the equator to 9.83 m/s² at the poles and drops with altitude. That is why the standard value 9.80665 m/s² is used as a reference, and exercises use 9.8 or 10 for simplicity.

Next steps

The free-fall formulas and what changes with g

Starting from rest, the distance fallen is h = g·t²/2, the speed is v = g·t and, without time, v² = 2·g·h. Solving, t = √(2h/g) and v = √(2·g·h). Mass does not appear: in a vacuum a bowling ball and a feather land together. A 45 m fall with g = 10 m/s² takes 3 s and ends at 30 m/s, which is 108 km/h. A 100 m fall with g = 9.80665 m/s² takes about 4.52 s and ends at about 44.3 m/s, or 159 km/h.

The value of g depends on the problem. 10 m/s² makes exercises easy, 9.8 m/s² is the usual school value and 9.80665 m/s² is standard gravity, exact by definition. On other bodies it changes a lot: 1.62 m/s² on the Moon and 3.73 m/s² on Mars (NASA fact sheets). A 10 m fall lasts 1.43 s on Earth with 9.80665, 2.32 s on Mars and 3.51 s on the Moon, arriving at 14.0, 8.64 and 5.69 m/s respectively.

If the object is thrown down rather than dropped, an initial speed enters: h = v₀·t + g·t²/2. Throwing a stone downward at 10 m/s from 15 m with g = 10 m/s² gives 5t² + 10t - 15 = 0, whose positive root is t = 1 s, and the stone arrives at 20 m/s. A neat pattern for motion from rest: in successive seconds the object covers distances in the ratio 1 : 3 : 5 : 7, that is 5 m, 15 m, 25 m and 35 m with g = 10 m/s².

The model ignores air. For short falls of dense objects the error is small, but for paper, leaves or skydivers drag grows with speed until it balances the weight, and the speed approaches a terminal value instead of growing without limit. The calculator gives the ideal case, which is what school exercises and most exams ask for.

Six falls worked out

45 m fall (g = 10)

Input: h = 45 m, g = 10 m/s²
Expected output: t = 3 s, v = 30 m/s

t = √(2·45/10) = 3 and v = 10·3.

100 m fall with standard g

Input: h = 100 m, g = 9,80665 m/s²
Expected output: t ≈ 4,52 s, v ≈ 44,3 m/s (159 km/h)

v = √(2·9.80665·100) = 44.29 m/s, times 3.6.

Height from the time

Input: t = 4 s, g = 10 m/s²
Expected output: h = 80 m, v = 40 m/s

h = 10·16/2 = 80.

10 m fall on the Moon

Input: h = 10 m, g = 1,62 m/s²
Expected output: t ≈ 3,51 s, v ≈ 5,69 m/s

A fall that lasts 1.43 s on Earth.

10 m fall on Mars

Input: h = 10 m, g = 3,73 m/s²
Expected output: t ≈ 2,32 s, v ≈ 8,64 m/s

Between Earth and the Moon.

Thrown downward

Input: v₀ = 10 m/s, h = 15 m, g = 10 m/s²
Expected output: t = 1 s, v = 20 m/s

The root t = -3 s of the quadratic is discarded.

Full tool FAQ

What is the difference between uniform motion and constant acceleration?

How do I convert km/h to m/s?

When should I use Torricelli's equation?

Which g should I use: 9.8, 10 or 9.80665?

How long does a free fall take and how fast does the object arrive?

How do I find the range and maximum height of an oblique launch?

Why do two different angles give the same range?

Why is average speed not the mean of the speeds?

What do two solutions or the negative time warning mean?

Does the calculator include air resistance?

Frequently asked questions

Continue in the tool

More pages for this tool

Free fall calculator: time, height and impact speed

The free-fall formulas and what changes with g

Six falls worked out

45 m fall (g = 10)

100 m fall with standard g

Height from the time

10 m fall on the Moon

10 m fall on Mars

Thrown downward

Full tool FAQ

Frequently asked questions

Does a heavier object fall faster?

How can I find the depth of a well by timing a drop?

Is gravity the same everywhere on Earth?

Next steps

Problem data

Positions (optional)

Result

Unit conversion (to SI)

Step by step

Graphs

Position vs time

Velocity vs time

Acceleration vs time

Continue in the tool

More pages for this tool

Free fall calculator: time, height and impact speed

The free-fall formulas and what changes with g

Six falls worked out

45 m fall (g = 10)

100 m fall with standard g

Height from the time

10 m fall on the Moon

10 m fall on Mars

Thrown downward

Full tool FAQ

Frequently asked questions

Does a heavier object fall faster?

How can I find the depth of a well by timing a drop?

Is gravity the same everywhere on Earth?

Next steps

Problem data

Positions (optional)

Result

Unit conversion (to SI)

Step by step

Graphs

Position vs time

Velocity vs time

Acceleration vs time