How to use this calculator

A projectile launched at an angle has horizontal and vertical velocity components. In an ideal constant-gravity model, the horizontal component stays constant and the vertical component changes with time. The positive ground-intersection time determines the horizontal range.

The method

x(t) = v cos(theta)t; y(t) = h + v sin(theta)t - gt^2/2

Enter the values in the labeled fields, check the units or selected mode, and choose Calculate. The result includes the applicable working and a breakdown or visual when useful. Change an input and calculate again to update the result.

WORKED EXAMPLE

Launch speed (m/s): 20 Launch angle (degrees): 45 Initial height (m): 0 Gravity (m/s^2): 9.80665

Horizontal range: 40.7886485191 m

Until the projectile reaches ground level y = 0.

Scope and limitations

No air resistance, wind, drag, spin, or changing gravity. Ground is at y = 0, launch height is nonnegative, and inputs use SI units. The result is an educational idealization, not a real-world trajectory guarantee.

Common questions

Can I launch from above ground level?

Yes. Enter a positive initial height to model a launch above y = 0.

Can the launch point downward?

Yes. Angles from -90 to 90 degrees are supported. A downward launch from ground level has no airborne time in this model.

References & further reading

External references provide background, not an endorsement of this implementation. See our methodology for numerical conventions and limitations.