Projectile Range Calculator

Projectile Range Calculator

Calculate the maximum horizontal distance a projectile travels on level ground.

Last updated: March 2026 | By ForgeCalc Engineering

Horizontal Range (R)
254.84
Meters (m)

What is Projectile Range?

The horizontal range of a projectile is the distance along the horizontal plane it travels from the launch point to the point where it returns to the same vertical level. This calculation assumes a flat surface and no air resistance.

The range depends on the initial velocity, the launch angle, and the acceleration due to gravity. It is a fundamental concept in ballistics and sports science.

The Formula

Range Formula (Level Ground)

R = (v₀² · sin(2θ)) / g
  • R = Horizontal Range
  • v₀ = Initial Velocity
  • θ = Launch Angle
  • g = Gravity (9.81 m/s²)

Frequently Asked Questions

Why is 45° the optimal angle?

The function sin(2θ) reaches its maximum value of 1 when 2θ = 90°, which means θ = 45°. This provides the best balance between horizontal velocity and time in the air.

How does air resistance change the range?

Air resistance (drag) significantly reduces the range and changes the trajectory from a perfect parabola to a more skewed shape. The optimal angle for maximum range also drops below 45°.

What if the ground is not level?

If the projectile lands at a different height than it started, you must use the full kinematic equations to solve for the time of flight first.

Does gravity vary on Earth?

Yes, gravity varies slightly by latitude and altitude, ranging from about 9.78 to 9.83 m/s². This can affect long-range ballistics.

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