Calculadora de Alcance de Projétil

R = v²·sin(2θ)/g — alcance máximo de projétil lançado na mesma altura.
Created by
Renato Passos, Eng. de Software
Reviewed by
Renato Passos, Eng. de Software

Last updated: Apr 18, 2026

Alcance R
91,74 m

Formula

R = v²·sin(2θ)/g

About this calculator

The Projectile Range Calculator determines the maximum horizontal distance traveled by a projectile launched from ground level, assuming launch and impact points are at the same height. The calculation uses the formula R = v²·sin(2θ)/g, where v is initial velocity, θ is launch angle, and g is gravity acceleration (usually 9.8 m/s²). This tool is useful for physics students, engineers, and enthusiasts wanting to predict projectile motion in parabolic paths.

Operation is straightforward: enter initial velocity (in m/s) and launch angle (in degrees). The calculator applies the formula and returns the range in meters. It assumes ideal conditions: no air resistance and constant gravity. Complementary angles (e.g., 30° and 60°) yield the same range, and maximum range occurs at 45°.

Use this calculator in scenarios such as estimating how far a soccer ball travels after a kick, calculating projectile range in ballistics games, or verifying kinematics exercises. It also aids in designing projectile launch experiments in physics labs.

Cautions: the formula ignores drag, wind, or gravity variations. For real-world accuracy (e.g., sports or ballistics), external factors may affect results. Also, the angle must be between 0° and 90°; outside this range, the projectile would have no positive range.

Frequently asked questions

What does the launch angle mean?

It is the angle between the initial velocity direction and the horizontal. For example, 45° gives maximum range for a given speed.

Can I use km/h for velocity?

The calculator expects m/s. Convert km/h to m/s by dividing by 3.6 before entering.

Why is the range zero for 0° or 90°?

At 0°, the projectile is launched horizontally and hits the ground immediately (if initial height is zero). At 90°, it goes straight up and down, with no horizontal displacement.

Does the calculator consider air resistance?

No. It uses the ideal model without drag. For real cases with resistance, the range is shorter.

What is the default gravity value used?

The default is 9.8 m/s², but you can change it if needed, for example, to simulate other planets.

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