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Projectile Motion Calculator
Calculate the range, maximum height, and flight time of a projectile from its launch speed and angle.
Calculator & Result
Estimate only. Confirm units and assumptions before using the result for a safety-critical decision.
How to Use This Calculator
- Review the default values and replace them with your own Initial velocity (m/s), Launch angle (degrees).
- Keep units consistent with the labels shown beside each field.
- Read the primary result first, then compare the supporting results and assumptions below it.
- Change one assumption at a time to see how sensitive the estimate is before using it in a real decision.
Detailed Breakdown
For a projectile launched at speed v and angle a (ignoring air resistance, using g = 9.81 m/s2): range = v^2 sin(2a) / g, maximum height = (v sin a)^2 / (2g), and flight time = 2v sin a / g. Enter the launch speed in m/s and the angle in degrees.
This page reports Range, Maximum height, Flight time. The first value is the headline estimate; the other values help you understand the calculation rather than acting as separate guarantees. Use the result as a comparison starting point, and test a conservative and an optimistic input set before relying on it.
Examples
Using the sample inputs (Initial velocity (m/s): 20; Launch angle (degrees): 45), the range is 40.7747. Change the inputs above to try your own values.
Assumptions and Limitations
- For a projectile launched at speed v and angle a (ignoring air resistance, using g = 9.81 m/s2): range = v^2 sin(2a) / g, maximum height = (v sin a)^2 / (2g), and flight time = 2v sin a / g. Enter the launch speed in m/s and the angle in degrees.
- Small changes in the inputs can materially change the output. Rounded values and measurement error may not be represented.
- Estimate only. Confirm units and assumptions before using the result for a safety-critical decision.
- Verify important results against an authoritative source or qualified professional before acting.
Frequently Asked Questions
What does the Projectile Motion Calculator calculate?
Calculate the range, maximum height, and flight time of a projectile from its launch speed and angle. For a projectile launched at speed v and angle a (ignoring air resistance, using g = 9.81 m/s2): range = v^2 sin(2a) / g, maximum height = (v sin a)^2 / (2g), and flight time = 2v sin a / g. Enter the launch speed in m/s and the angle in degrees.
How should I use the result?
Use it to compare scenarios and identify the inputs that matter most. Recalculate after changing assumptions, and do not treat an estimate as a quote, diagnosis, approval, or guarantee.
Why might my real-world result be different?
Actual results can differ because of rounding, measurement error, friction, air resistance, or conditions that are not included in this simplified model.
Can I rely on this estimate as a final decision?
No. Review the displayed assumptions and verify important results with an appropriate professional or authoritative source before acting.
