About the Projectile Motion Calculator
A ball thrown, a stone skimmed or a rocket fired follows a curved path called a parabola. This calculator takes the launch speed, the launch angle and the starting height, and gives the time in the air, how far the object travels sideways and the highest point it reaches. It also shows the speed at which it lands. Type the launch speed, the launch angle, the starting height and the gravity and the range of a projectile appears at once, with a few related figures underneath, and you can copy the result with one tap. The sums run in your browser, so nothing you enter is uploaded.
Updated October 2026
How to use the Projectile Motion Calculator
- 1Enter the launch speed, the launch angle, the starting height and the gravity.
- 2Pick the units or options from the menus if the range of a projectile tool offers them.
- 3Read the range of a projectile in the large result box.
- 4Look at the extra rows for related figures.
- 5Press Copy result to keep the answer.
When you need the range of a projectile
Sports analysts use projectile motion to study throws, kicks and jumps. Engineers use it for water jets, sprinklers and fireworks, and teachers use it to show how horizontal and vertical motion are independent of each other.
Starting from a height, such as a cliff or a window, makes the flight longer, and the tool handles it. An angle below zero throws the object downwards. On the Moon, where gravity is weaker, the same throw goes about six times as far.
How the range of a projectile is worked out
Horizontal speed = v × cos(angle) and vertical speed = v × sin(angle). Time in the air solves height = start + vertical speed × t − ½ g t². Range = horizontal speed × time. Maximum height = start + vertical speed² ÷ (2g). A ball launched at 20 m/s at 45° from the ground flies for 2.88 s, travels 40.79 m and reaches 10.20 m. At 30° it goes 35.32 m and at 60° also 35.32 m, because angles that add up to 90° give the same range on level ground.
Every answer on this page comes from that one rule, so you can check any result by hand with a calculator. The figures shown underneath, such as other units, are conversions of the same answer.
- Launch angle from -90° to 90°
- Starting height
- Landing speed shown
Mistakes to avoid with range of a projectile
The model ignores air resistance, wind and spin. Real balls with high speeds or big surfaces fall short of the predicted range, and a golf ball with backspin can fly far higher than the simple parabola suggests. Use the results as a good estimate for compact objects at moderate speeds.
On phone and computer
On a phone, type into the boxes one after another and read the range of a projectile underneath; Copy result puts it on the clipboard for a message or a note. On a computer the inputs sit on the left and the answer on the right, so you can change one figure and watch the range of a projectile move. The projectile motion calculator works the same on both. Break the path into parts with Trigonometry Calculator for the angle, Distance Calculator and Speed Calculator for the ground movement, and Free Fall Calculator for a drop with no sideways motion.
Features
- 45° is best on level ground
- Complementary angles match
- Air resistance shortens real throws
- Clear messages when the range of a projectile inputs make no sense
- Copy the result with one tap
- Private: nothing is uploaded
Frequently asked questions
How do I calculate range of a projectile?
Horizontal speed = v × cos(angle) and vertical speed = v × sin(angle). Time in the air solves height = start + vertical speed × t − ½ g t². Range = horizontal speed × time. Maximum height = start + vertical speed² ÷ (2g). A ball launched at 20 m/s at 45° from the ground flies for 2.88 s, travels 40.79 m and reaches 10.20 m. At 30° it goes 35.32 m and at 60° also 35.32 m, because angles that add up to 90° give the same range on level ground.
What is the formula for range of a projectile?
Horizontal speed = v × cos(angle) and vertical speed = v × sin(angle). Time in the air solves height = start + vertical speed × t − ½ g t². Range = horizontal speed × time. Maximum height = start + vertical speed² ÷ (2g). The projectile motion calculator applies it exactly and rounds only the displayed answer to six significant figures.
Which angle gives the longest range?
On level ground, 45°. With a starting height above the landing point, a slightly lower angle is best.
Does the mass of the object matter?
Not without air resistance. A heavy and a light ball launched the same way follow the same path.
What is the impact speed?
The speed at which the object lands. It equals the launch speed when the launch and landing heights are equal.
Is this projectile motion calculator free and private?
Yes. It is free, needs no account and runs in your browser, so the numbers you type are not uploaded or stored.