What about air resistance?

Drag is significant at high speeds (>30 m/s). Real projectiles peak around 30-40°, not 45°.

Different launch and landing height?

This calc assumes level ground. With Δh: solve quadratic in t. More complex.

Parabola — symmetric around peak. Apex at half-flight time.

Real-world projectile design?

Mortars: ~45°. Artillery: 35-45° depending on range. Football kick-off: ~55° to give air time.

Projectile Motion Calculator

Range, max height, time of flight from launch speed and angle (level ground, no air drag).

Result

Range

91.743 m

Max height 22.936 m, time 4.325 s.

v₀30 m/s
θ45°
v_x = v₀ cos θ21.2132 m/s
v_y = v₀ sin θ21.2132 m/s
Time of flight4.3248 s
Max height22.9358 m
Range91.7431 m

Step-by-step

v_x = v₀ cos θ = 21.2132 m/s.
v_y = v₀ sin θ = 21.2132 m/s.
Time of flight = 2 v_y / g = 4.3248 s.
Range = v_x × t = 91.7431 m.
Max height = v_y² / (2g) = 22.9358 m.

How to use this calculator

Enter launch speed and angle.
Read range + max height + flight time.

About this calculator

Projectile motion (no air resistance) on level ground: horizontal velocity constant; vertical velocity changes with gravity. Max range at θ = 45°. Symmetric launch ↔ landing. Range = v₀² sin(2θ)/g. Real projectiles (baseballs, bullets, golf balls) deviate due to air drag — drag scales with v², so high-speed projectiles fall short of vacuum prediction.