About the Projectile Motion Calculator
What is the Projectile Motion Calculator?
A thrown ball, a cricket shot or a water jet follows a parabola. This projectile motion calculator splits the launch velocity into horizontal and vertical parts and works out how far and how high the projectile goes.
It handles launches from a height, such as a ball thrown from a balcony, and other planets' gravity.
How to use the Projectile Motion Calculator
- Launch Speed (m/s) (sample: 20)
- Launch Angle (°) (sample: 45)
- Launch Height above the Ground (m) (sample: 0)
- Gravity (sample: Earth (9.807 m/s²))
- Press Calculate Projectile Motion (results also refresh as you type). The result card shows the Horizontal Range, along with Time of flight, Maximum height, Time to maximum height and Impact speed.
Formula used
Range = vₓ × t; t = (v_y + √(v_y² + 2gh₀)) ÷ g
- vₓ, v_y = v cos θ and v sin θ
- Max height = h₀ + v_y² ÷ 2g
From ground level, range = v² sin 2θ ÷ g, greatest at 45°.
Worked example
These are the sample values already filled in the calculator above, and the result it returns for them:
| Input | Sample value |
|---|---|
| Launch Speed (m/s) | 20 |
| Launch Angle (°) | 45 |
| Launch Height above the Ground (m) | 0 |
| Gravity | Earth (9.807 m/s²) |
| Result | Value |
|---|---|
| Horizontal Range | 40.789 m |
| Time of flight | 2.884 s |
| Maximum height | 10.197 m |
| Time to maximum height | 1.442 s |
| Impact speed | 20 m/s |
| Note | Ignores air resistance; real ranges are shorter |
Tips for using the Projectile Motion Calculator
- Air resistance shortens real ranges, especially for light, fast objects.
- Complementary angles (30° and 60°) give the same range from ground level.