How to use (3 steps)
- Choose the mode: compute trajectory or find the speed for a target range.
- Enter speed/angle/heights/gravity (example values are prefilled).
- Press Compute to see time of flight, range, height, and the trajectory table. Copy URL shares the setup.
Default example values are prefilled. Press Compute to generate flight time, range, maximum height, steps, and the trajectory table.
Inputs
Results
Flight time 2.8832 s and range 40.7747 m for the default 20 m/s, 45° launch.
| Initial speed | 20 m/s |
|---|---|
| Launch angle θ | 45 deg |
| Time of flight t_f | 2.8832 s |
| Range R | 40.7747 m |
| t (s) | x (m) | y (m) |
|---|---|---|
| 0 | 0 | 0 |
| 0.7208 | 10.1937 | 7.6453 |
| 1.4416 | 20.3874 | 10.1937 |
| 2.8832 | 40.7747 | 0 |
How it's calculated
- Solve the vertical quadratic for the positive flight time t_f = 2.8832 s.
- Compute range from x(t_f) = v₀ cos θ · t_f = 40.7747 m.
- Peak height occurs halfway through this symmetric flight, giving y_max = 10.1937 m.
Use this page when launch angle and flight path are the main question
Start here when you want range, flight time, peak height, or target reachability from one launch setup under ideal projectile assumptions. Open Circular Motion for orbit-style motion, Simple Harmonic Motion for periodic systems, and Snell's Law when the problem is angle-based optics rather than mechanics.
- Keep one unit system throughout the run so the interpretation stays clean.
- Change only one launch input at a time when comparing trajectories.
- Use the target-point check as a feasibility screen before doing manual algebra.
FAQ
Does this calculator consider air resistance?
No. It assumes ideal projectile motion without air drag, suitable for quick textbook-style estimates.
How should I handle units?
Use any consistent unit system (all distances and speeds in the same units). Defaults are meters and m/s.
What if the target point cannot be reached?
Some combinations of angle and heights make the target unreachable. The calculator will show an error if so.
What should I enter first for projectile motion?
Enter initial speed, launch angle, height, and gravity first. Keep air resistance assumptions clear because this calculator models the idealized trajectory.
Why can projectile motion results differ from nearby tools?
Differences usually come from initial speed, launch angle, height, gravity, and drag-free model assumption. Match those assumptions before comparing this result with another CalcBE page, spreadsheet, or external tool.
Related calculators
- Circular motion & centripetal force calculatorCompare horizontal and vertical motion ideas with uniform circular motion and centripetal force.
- Ideal Gas Law Calculator with Steps | CalcBESwitch to gas-law problems when you need another physics tool with step-by-step unit-based inputs.
- Simple harmonic motion (SHM) calculatorUse this for another introductory mechanics model focused on periodic motion and restoring forces.
- Simple Harmonic Motion Simulator | CalcBEVisualize oscillation and compare it with the time-based motion patterns used in projectile problems.
- Snell's law Refraction Calculator | CalcBEExplore another angle-based physics calculator when you want to compare geometry across topics.
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