Projectile Range Calculator

A projectile launched at speed v₀ and angle θ travels a horizontal range R = v₀²·sin(2θ)/g. Enter any two values to solve for the third. When solving for the angle, the calculator returns the low-angle solution (a second, high-angle solution gives the same range).

How to interpret the result

Range grows with the square of launch speed — doubling v₀ quadruples the range. The sin(2θ) factor peaks at θ = 45°, which is why 45° gives maximum range on flat ground.

Assumptions

• No air resistance (ideal projectile)
• Flat ground — launch and landing at the same height
• g = 9.81 m/s²
• The angle solution is the low-angle one (0–45°); a second high-angle solution exists by symmetry