Physics
Projectile Motion
Model ideal projectile motion (no drag) by entering an initial velocity, launch angle, and starting height. The calculator reports flight time, range, and peak altitude.
Model range, flight time, and peak height for a launch angle in standard gravity.
Kinematics
x(t) = v cosθ · t y(t) = h₀ + v sinθ · t − ½ g t²
Flight time solves the quadratic y(t) = 0. Range = x(time). Peak height occurs at t = (v sinθ)/g.
How to use
- Enter the launch speed (m/s), launch angle (degrees), and optional initial height.
- Adjust gravity if you need a different planetary body.
- Read the time of flight, horizontal range, peak height, and x-distance at the apex.
Example
Input: v = 30 m/s, θ = 45°, h₀ = 0 m
Output: Time ≈ 4.33 s, Range ≈ 91.8 m, Peak height ≈ 22.9 m
Student-friendly breakdown
This walkthrough emphasizes the most searched ideas for Projectile Motion: Projectile Motion. Start with the formula above, then follow the guided steps to double-check your work. For quick revision, highlight the givens, plug into the equation, and finish by verifying your units.
Need more support? Use the links below to open the long-form guide, browse additional examples, or hop into adjacent calculators within the same topic — each one is a quick way to double-check your work or handle a related question without starting from scratch.
Deep dive & study plan
Projectile Motion: Range, time of flight, and peak height for a launch angle. It's built around projectile, ballistics, trajectory, so you can go from a raw question to a checked answer without switching tools.
The math behind it: Flight time solves the quadratic y(t) = 0. Range = x(time). Peak height occurs at t = (v sinθ)/g. The core relationship is x(t) = v cosθ · t y(t) = h₀ + v sinθ · t − ½ g t², shown above the calculator so you can see exactly how your inputs turn into the result.
To use it well: (1) Enter the launch speed (m/s), launch angle (degrees), and optional initial height. (2) Adjust gravity if you need a different planetary body. (3) Read the time of flight, horizontal range, peak height, and x-distance at the apex. Keep your units consistent as you go, and re-run a case you already know the answer to — it's the fastest way to catch a typo before it throws off a result you're relying on.
Worked example: entering v = 30 m/s, θ = 45°, h₀ = 0 m returns Time ≈ 4.33 s, Range ≈ 91.8 m, Peak height ≈ 22.9 m. Try swapping in your own numbers next, especially a case you're unsure about, before you use this for something that matters.
Quick retention checklist
- Speak the formula aloud (or annotate it) so the relationships stick.
- Write each step in your own words and compare with the numbered list above.
- Swap in new numbers for the Example to make sure the calculator (and your logic) handles edge cases.
- Check at least one related calculator below — it's the fastest way to confirm your numbers still line up from a different angle.
FAQ & notes
Does it include drag or spin?
No—this is the textbook vacuum solution. For drag or Magnus effects, use a dedicated trajectory simulator.
Can I use degrees greater than 90?
Angles must be between 0° and 90°. Negative angles represent downward launches; convert as needed.
What formula does the Projectile Motion use?
Flight time solves the quadratic y(t) = 0. Range = x(time). Peak height occurs at t = (v sinθ)/g.
How do I use the Projectile Motion?
Enter the launch speed (m/s), launch angle (degrees), and optional initial height. Adjust gravity if you need a different planetary body. Read the time of flight, horizontal range, peak height, and x-distance at the apex.