Projectile Range
Model ideal flight landing at the launch height.
Your numbers
Horizontal range
Same launch and landing height, constant gravity, no drag, wind or Earth curvature.
Scenario comparison
Up to three snapshots in this tab. Loading one replaces the current inputs.
Formula
Use R = v²sin(2θ)/g and t = 2v sinθ/g. v is launch speed in m/s, θ is elevation in degrees, and g is gravity in m/s². Range R is in m and flight time t is in s, with equal launch and landing heights and no air resistance.
Model ideal flight landing at the launch height.
Worked example
- Launch speed (m/s)
- 20
- Launch elevation (degrees)
- 45
- Gravity (m/s²)
- 9.80665
- Horizontal range
- 40.7886485191 m
- Flight time
- 2.88419299633 s
- Maximum rise
- 10.1971621298 m
Scope and limitations
Same launch and landing height, constant gravity, no drag, wind or Earth curvature.
Inputs are checked for missing values and allowed ranges. A result outside the finite numeric range is not displayed. Rounding affects display, while the calculation uses the model’s numeric precision.
Check your units and assumptions before relying on a result. Changing a label does not convert a currency or physical unit.
Formula version: 5cb3f6cc6570 · Example checked: