Projectile Motion
Calculate projectile range, peak height, flight time, and impact speed from launch inputs.
Launch Parameters
Calculator guide
Projectile Motion Calculator
Estimate a launched object's range, peak height, flight time, impact speed, and several related values from launch speed, angle, launch height, gravity, mass, drag coefficient, air density, and cross-sectional area. This page uses simplified equations rather than a full aerodynamic simulation.
How to use the calculator
- 1Enter launch speed, angle, launch height, and local gravitational acceleration in the displayed units.
- 2Enter mass, drag coefficient, air density, and frontal area for the drag estimate; confirm all values use the units requested by the fields.
- 3Calculate and inspect range, height, time, impact speed, and impact force. Treat the output as a model estimate, not a measured trajectory.
Important details to understand
1.Start with the right inputs
Check every number, date, unit, and selected mode before calculating. A correct formula can still give a misleading answer when an input is missing, entered in the wrong unit, or based on a different time period.
2.Know what the calculation includes
The method below describes what this tool uses. Real situations can involve extra rules, costs, calendar conventions, or personal details that are not part of the form, so compare the assumptions with your actual question.
3.Read the unit and rounding
Look at the label as well as the displayed number. Rounding can change the last digits, and results in different units or time periods are not directly comparable until you convert them consistently.
4.Treat the result as a useful check
Use the output to understand a calculation, explore a scenario, or make an initial estimate. When a result affects a formal deadline, a health decision, a contract, or a large payment, confirm it with the relevant source or qualified professional.
How the calculation works
The tool resolves velocity into horizontal and vertical components, computes ideal vertical flight time under constant gravity, and estimates drag deceleration from drag coefficient, air density, area, and mass. It then adjusts the horizontal range using an average-deceleration approximation. Impact force is estimated from momentum change over a fixed 0.1-second duration.
A worked example
At a fixed launch speed and height, changing the angle changes the horizontal and vertical velocity components, so both range and peak height can change.
When this calculator is useful
Explore introductory mechanics, compare hypothetical launch conditions, and see how angle or launch height affects an idealized result.
Planning ahead
Try a few realistic input values to see how a change in an amount, measurement, date, or rate affects the answer.
Learning the method
Follow the explanation and example to understand which inputs matter and how they are combined.
Checking your own work
Compare the result with a hand calculation, a worksheet, or a trusted source when you need an independent sense check.
Explaining a result
Keep the original inputs and units with the output so another person can understand what was calculated.
Tips for a more reliable answer
- Enter the values from the same source and keep units consistent throughout the calculation.
- Check that you selected the mode or option that matches the question you are trying to answer.
- Use the worked example to confirm you understand the inputs and the kind of result the tool returns.
- Save the inputs with the result so you can review or repeat the calculation later.
Limitations and assumptions
The drag and impact-force sections are rough approximations. Wind, lift, spin, changing drag, terrain, object shape, and actual stopping time are not modeled accurately. Do not use this for weapons, safety decisions, or predicting a real object's impact; use validated physics methods and measurements.
Every result depends on the information entered and the method described above. The calculator cannot confirm that the inputs are complete or that its assumptions match a particular provider, policy, location, body, or real-world situation.
Frequently asked questions
Does this include air resistance?
It applies a simplified average horizontal drag adjustment, not a full time-stepped aerodynamic model.
Why is impact force uncertain?
The result assumes a fixed 0.1-second impact duration; real force depends strongly on how the object stops.
Can I use this for a real projectile?
Treat it as an educational estimate only; real conditions and model limitations can produce large differences.
Why might my result differ from another calculator?
Tools can use different assumptions, units, date conventions, included costs, or rounding rules. Compare the inputs and method descriptions before deciding that one result is wrong.
What should I check if the answer looks wrong?
Review the selected mode, each entered value, the units, and any optional fields. Then compare a simple example with the method described in this guide.
Can I rely on the result for an official or high-impact decision?
Use the result as an estimate or explanation and check the limitations listed for this tool. Confirm important decisions with the relevant official source or a qualified professional.