Projectile Range at 60° Calculator

Calculate horizontal distance for a launch angle of sixty degrees with rigorous math unit conversions and gravity presets. Enter speed and height choose Earth Moon or Mars and receive range time of flight and velocity components with error checks suitable for study labs and engineering practice fieldwork demonstrations tutorials projects classrooms and experiments scenarios

Inputs

Results

Range: 79.479013 m (260.757917 ft)
Time of flight: 5.298601 s
Horizontal speed (v_x): 15.000000 m/s
Initial vertical speed (v_y0): 25.980762 m/s
Peak time: 2.649300 s
Maximum height: 34.415422 m

All calculations assume flat terrain and constant gravity.

Derivation at 60°

Using angle θ = 60°, sin60 = √3/2 and cos60 = 1/2.

Time to impact for launch height y₀ ≥ 0:

t = (v·sinθ + √((v·sinθ)² + 2·g·y₀)) / g

Horizontal range:

R = v·cosθ · t

For level ground (y₀ = 0), this reduces to R = (v² · sin(120°)) / g = (v² · √3/2) / g.

FAQs

1) What assumptions does this tool make?

It assumes no air drag, constant gravity, flat landing surface, and a fixed launch angle of 60°.

2) Can I change the planet or gravity?

Yes. Select Earth, Moon, Mars, or enter a custom gravitational acceleration.

3) How are different speed units handled?

The input is converted to meters per second internally. You can enter m/s, km/h, or ft/s.

4) What does launch height change?

Positive launch height increases flight time and therefore can increase the range compared with level-ground launch.

5) Why is my result zero?

Range is zero when launch speed is zero or gravity is set to an invalid value.

6) What about angles other than 60°?

This page focuses on 60°. To analyze other angles, modify the formulas or use a general-angle variant.

Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.