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DIY Cost Tools

DIY Cost Tools

Projectile Motion Calculator

Model an ideal projectile that launches and lands at the same elevation. Supply the initial speed, launch angle measured above horizontal and the local gravitational acceleration.

Enter every field, including explicit zeros when permitted. Decimal and scientific notation are accepted; commas, fractions and blanks are rejected. Each input must be finite and no larger than 1 billion in absolute value. Observe the stated units and domain limits.

Flight time (s)2.884192996
Horizontal range (m)40.78864852
Maximum height (m)10.19716213

How to use this calculator

  1. Enter every quantity in the unit printed beside its field.
  2. Select Calculate or press Enter.
  3. Read the labeled results and compare them with the assumptions below.

Formula and method

For equal launch and landing heights: t = 2v sin θ/g, R = v² sin(2θ)/g, and h = v² sin²θ/(2g).

The calculation runs locally in your browser. If any entry is invalid or a mathematical condition is undefined, the prior result is hidden so it cannot be mistaken for a new answer.

Worked example

Using Launch speed (m/s) = 20, Launch angle (degrees) = 45, Gravitational acceleration (m/s²) = 9.80665, the formula returns Flight time (s) = 2.884192996, Horizontal range (m) = 40.78864852, Maximum height (m) = 10.19716213. The displayed default result is generated from these same inputs.

Limitations and safety

Ignores air resistance, lift, wind, Earth curvature and height differences. It is not a ballistics or safety-planning tool; real trajectories can differ substantially. Results use floating-point arithmetic and are displayed to about 10 significant digits; measurement uncertainty usually supports fewer. Verify units before relying on a result.

Frequently asked questions

When does the range formula apply?

Only when launch and landing heights match and constant downward gravity is the only acceleration.

Why might a measured result differ?

The formula isolates the stated model. Real systems can add uncertainty, losses, changing properties, geometry or forces that are not among the inputs.

How should I handle units?

Convert every value to the unit shown beside its field before calculating. A numerically valid value in the wrong unit will still produce a wrong result.

Review notes and reference

Reviewed October 3, 2026. The default example and an independent edge or scaling case were checked against expected values. The live script was also checked for blank, text, comma-formatted, non-finite and out-of-range entries. Method reference. Constants use the values stated in the formula. This page’s explanation and example are original.

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