Projectile Motion Calculator
Calculate flight time, horizontal range, peak height and impact velocity for a thrown object. Enter launch height and gravity, mix units and inspect the trajectory.
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Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Resolve initial velocity into horizontal and vertical components. Solve the vertical quadratic for the time when height first returns to the landing plane, then apply that time to horizontal motion. The vertical component reaches zero at the apex when the initial motion is upward.
x=v cosθ·t; y=h+v sinθ·t−gt²/2; landing occurs at y=0
Worked example
At20m/s,30° and zero initial height withg=9.8m/s², flight time is about2.040816s, range35.347976m and peak height5.102041m. A vertical throw has zero horizontal range.
Assumptions and input details
Ideal point-object model with constant gravity, a flat landing plane and no air resistance, wind, lift or spin. Initial height is nonnegative and angle lies between−90° and90°. Downward or horizontal release at zero height lands immediately. Speed is limited to1e6m/s, height1e9m and gravity1e−9–1000m/s². Trajectory axes are scaled independently; use their numeric labels rather than judging angles from the chart. Results are model calculations, not measured performance.
References: OpenStax projectile motion
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Choose from 23 length definitions, including explicitly labelled regional measures. Area conversions square the length factor; geometric volumes cube it.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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