Why are there two angles?

A reachable target can often be hit by a low, fast trajectory or a higher, longer trajectory.

Is 45 degrees always best?

No. Forty-five degrees maximizes ideal range only when launch and landing heights are equal.

Can the angle be negative?

Yes. A high launch point with short flight time can require aiming below the horizon.

Launch Angle Calculator

Find projectile launch angles for a target point, obstacle clearance, or a known range and flight time.

Calculation mode

Angle to hit a point Angle with obstacle Angle from range and time

Initial speed, m/s

Target distance, m

Target height, m

Launch height, m

Gravity

standard 9.80665 classroom 9.8 rounded 10

Calculation uses an ideal no-air-resistance model without wind or spin. Light objects and high speeds usually travel lower and shorter in real life.

To find an angle for a target range, use this mode with target height set to zero.

Low-angle trajectory

32.78°

High-angle trajectory

68.53°

Low trajectory

Time to target1.9 s

Maximum height9.34 m

Horizontal velocity21.02 m/s

Vertical velocity13.53 m/s

High trajectory

Time to target4.37 s

Maximum height27.6 m

Horizontal velocity9.15 m/s

Vertical velocity23.27 m/s

Find the launch angle for a projectile

The English intent is an inverse projectile-motion solver: the target, obstacle, or flight time is known, and the launch angle must be found.

y = h_{0} + x tan θ - \frac{g x ^{2}}{2 v _{0}^{2} cos ^{2} θ}

theta is the launch angle, v0 is initial speed, x is horizontal distance and h0 is launch height.

When a target point is reachable, the ideal model can return a low-angle and a high-angle trajectory.

Model limits

Ideal projectile model

This calculator ignores air resistance, wind, spin, lift and object shape. Use it for classroom physics and rough estimates only.

Frequently Asked Questions

Sources and References

Calculations are based on the listed reference sources. Links open in a new tab.

Updated: June 2, 2026

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