Enter your launch speed, launch angle, and initial height to calculate the horizontal range of a projectile. The Projectile Range Calculator returns the total distance traveled, maximum height reached, and time of flight — all based on standard kinematic equations with no air resistance.
Horizontal Range
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Maximum Height
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Time of Flight
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Horizontal Velocity (V₀ₓ)
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Vertical Velocity (V₀ᵧ)
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The range of a projectile is the total horizontal distance it travels from the launch point until it hits the ground. It depends on the launch speed, launch angle, initial height, and gravitational acceleration. Maximum range on flat ground (initial height = 0) is achieved at a 45° launch angle.
For a launch from the ground, the range formula is d = (V₀² × sin(2θ)) / g. When launched from an initial height h, the formula becomes d = V₀cosθ × [V₀sinθ + √((V₀sinθ)² + 2gh)] / g. This calculator handles both cases automatically based on your inputs.
When launched from the ground (initial height = 0), a 45° angle always produces the maximum range. However, if the projectile is launched from an elevated position, the optimal angle for maximum range is slightly less than 45°, depending on the height and launch speed.
No — when air resistance is neglected, the mass of a projectile has no effect on its range. The equations of projectile motion depend only on initial velocity, launch angle, initial height, and gravitational acceleration. This is consistent with Galileo's principle that all objects fall at the same rate regardless of mass.
For a projectile launched from the ground, the minimum range (approaching zero) occurs at 0° (horizontal launch with no vertical component to keep it airborne) or 90° (straight up, so it falls back to the launch point). In practice, a very small or very large angle both reduce the range significantly.
A greater initial height increases the time of flight because the projectile has more vertical distance to fall before hitting the ground. This longer flight time translates directly into a greater horizontal range, even at the same launch speed and angle.
Yes — lower gravity (like on the Moon) increases range significantly because the projectile stays airborne longer. Higher gravity reduces range. This is why a ball thrown on the Moon would travel about 6 times farther than the same throw on Earth.
This calculator assumes no air resistance, a flat Earth surface, and constant gravitational acceleration throughout the flight. These are standard assumptions for introductory physics problems. Real-world projectiles (especially at high speeds or long distances) are affected by drag, wind, and Earth's curvature.