About this calculator
Enter the launch speed, angle and optional starting height to find how far it travels, how high it goes, how long it is in the air and how fast it lands.
It ignores air resistance, as in school physics. You can choose the gravity of Earth, the Moon, Mars or Jupiter.
Worked examples
Real numbers, worked out by the same calculator. Press “Use these numbers” to try one above.
20 m/s at 45° from the ground
- Range (horizontal distance)
- 40.788649 m
- Time of flight
- 2.884193 s
- Maximum height
- 10.197162 m
- Speed on landing
- 20 m/s
Launched at 20 m/s and 45° from 0 m on Earth, it flies for 2.884193 s, reaches 10.197162 m and lands 40.788649 m away (ignoring air resistance).
Show the working
- Split the speed: horizontal = 20 × cos 45° = 14.142136 m/s; vertical = 20 × sin 45° = 14.142136 m/s.
- Time of flight from 0 m: t = (vertical + √(vertical² + 2 × g × height)) ÷ g = 2.884193 s.
- Range = horizontal speed × time = 14.142136 × 2.884193 = 40.788649 m.
- Maximum height = start + vertical² ÷ (2g) = 0 + 200 ÷ 19.6133 = 10.197162 m.
- Air resistance is ignored, so real projectiles fall short of these figures.
Thrown at 15 m/s and 30° from a 2 m height
- Range (horizontal distance)
- 22.878316 m
- Time of flight
- 1.761174 s
- Maximum height
- 4.867952 m
- Speed on landing
- 16.255048 m/s
Launched at 15 m/s and 30° from 2 m on Earth, it flies for 1.761174 s, reaches 4.867952 m and lands 22.878316 m away (ignoring air resistance).
Show the working
- Split the speed: horizontal = 15 × cos 30° = 12.990381 m/s; vertical = 15 × sin 30° = 7.5 m/s.
- Time of flight from 2 m: t = (vertical + √(vertical² + 2 × g × height)) ÷ g = 1.761174 s.
- Range = horizontal speed × time = 12.990381 × 1.761174 = 22.878316 m.
- Maximum height = start + vertical² ÷ (2g) = 2 + 56.25 ÷ 19.6133 = 4.867952 m.
- Air resistance is ignored, so real projectiles fall short of these figures.
The same 20 m/s at 45° on the Moon
- Range (horizontal distance)
- 246.91358 m
- Time of flight
- 17.459427 s
- Maximum height
- 61.728395 m
- Speed on landing
- 20 m/s
Launched at 20 m/s and 45° from 0 m on the Moon, it flies for 17.459427 s, reaches 61.728395 m and lands 246.91358 m away (ignoring air resistance).
Show the working
- Split the speed: horizontal = 20 × cos 45° = 14.142136 m/s; vertical = 20 × sin 45° = 14.142136 m/s.
- Time of flight from 0 m: t = (vertical + √(vertical² + 2 × g × height)) ÷ g = 17.459427 s.
- Range = horizontal speed × time = 14.142136 × 17.459427 = 246.91358 m.
- Maximum height = start + vertical² ÷ (2g) = 0 + 200 ÷ 3.24 = 61.728395 m.
- Air resistance is ignored, so real projectiles fall short of these figures.
How it works
Split the launch speed into a horizontal part v·cos θ (which stays constant) and a vertical part v·sin θ (which gravity changes). The time in the air comes from the vertical motion, and the range is horizontal speed × time.
- Maximum height = start height + (v·sin θ)² ÷ 2g
- On flat ground, time of flight = 2·v·sin θ ÷ g and range = v² · sin 2θ ÷ g
The best angle
On level ground the longest range comes from launching at 45°. Launching from a height makes the best angle a little lower. At 45° with 20 m/s on Earth, the range is about 40.8 m; on the Moon the same throw goes about six times as far.
What it ignores
Real projectiles are slowed by air resistance and affected by spin and wind, so they fall well short of these figures. The results are an idealised guide.
Frequently asked questions
What angle gives the longest range?
45° on level ground, ignoring air resistance.
How do I find the flight time?
On flat ground, t = 2 × v × sin θ ÷ g.
Does it include air resistance?
No. It uses the simple model taught in physics courses.
Why does the Moon give such a long range?
Gravity there is about a sixth of Earth's, so things stay in the air six times longer.
Formulas tested against hand-worked answers. Last reviewed 29 September 2026. These calculators do arithmetic only; they are not financial, tax or legal advice.