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Free Fall Calculator

Find how fast an object hits the ground and how long it takes to fall from a height. The free fall calculator also handles an object thrown up or down at the start, and leaves out air resistance, as most physics problems do.

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Units

Use 0 for an object that is dropped.

Thrown

9.81 m/s² (32.17 ft/s²) at Earth's surface. Many textbooks use 9.8.

Speed at the ground
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How to use the Free Fall Calculator

  1. Pick Meters or Feet.
  2. Enter the Height above the ground and the Starting speed. Use 0 for an object that is dropped.
  3. Choose whether it was thrown Downward or Upward.
  4. Keep gravity at 9.81 m/s², or type the value your course uses, such as 9.8.
  5. Read the speed at the ground, the vertical velocity with its sign, and the time it takes.

How it works

v = √(v0² + 2gh)
t = (u + v) ÷ g, where u = +v0 thrown up, −v0 thrown down
highest point = h + v0² ÷ (2g), when thrown up

Up is positive, so the vertical velocity at the ground is the speed with a minus sign. The speed is the same whether the object starts moving up or down at v0: an object thrown up passes its starting point on the way down at the same speed. Only the time changes.

Examples

  • A ball thrown down at 1.1 m/s from a 41 m roof, with g = 9.8 m/s²: v = √(1.1² + 2 × 9.8 × 41) = 28.37 m/s, so the vertical velocity is −28.37 m/s and it lands after 2.783 s.
  • A stone dropped from 20 m with g = 9.81 m/s²: 19.81 m/s after 2.019 s.
  • Thrown up at 5 m/s from 10 m: it rises to 11.27 m above the ground and lands at 14.87 m/s after 2.026 s.

Signs and which way is up

Physics problems usually take up as positive. A velocity of −28.37 m/s then means 28.37 m/s downward. If your problem takes down as positive, drop the minus sign. The speed has no direction, so it is the same either way.

Limitations

  • No air resistance. Light objects and long falls reach a top speed well below the result.
  • Gravity is treated as constant over the whole height.
  • Motion is straight up or down. For a throw at an angle, enter only the vertical part of the starting speed.

Frequently asked questions

How do you calculate the speed of a falling object?

Use v = √(v0² + 2gh). An object dropped from 20 m with g = 9.81 m/s² hits the ground at about 19.81 m/s.

Why is the vertical velocity negative?

Because up is taken as positive. A negative value means the object is moving down.

Should I use 9.8 or 9.81 for gravity?

Use the value your course or textbook uses. Standard gravity is 9.80665 m/s², often rounded to 9.81 or 9.8.

How long does it take to fall 100 meters?

Dropped with no air resistance and g = 9.81 m/s², about 4.52 seconds, reaching 44.29 m/s.

Often used together with Free Fall Calculator.