Mathematics · Mathematical Physics
Projectile Motion Calculator
Calculate ideal launch components, flight time, maximum height and horizontal range.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Resolve velocity: vx=20cos(45°)=14.142135623730951; vy=20sin(45°)=14.14213562373095.
- Flight time=2×14.14213562373095÷9.80665=2.8841929963302353; maximum height=10.197162129779281.
- Range=14.142135623730951×2.8841929963302353=40.78864851911713.
Problem → model → reason → result
What problem does this model solve?
Calculate ideal launch components, flight time, maximum height and horizontal range.
Why does the model apply?
Horizontal velocity stays constant while gravity changes vertical velocity, allowing the motion to be separated into perpendicular components.
What assumptions does it make?
Values use the displayed units, the named classical model describes the system, and idealisations such as constant acceleration, point particles or negligible drag apply where stated.
Formula
T=2v sinθ/g; H=v²sin²θ/(2g); R=v²sin2θ/g
Calculation and working
The calculator above substitutes your inputs into the model and leaves the calculation steps visible so the answer can be checked rather than merely accepted.
What does the result mean?
The result answers the stated problem in the units implied by your inputs. Read its sign, size and units together, then compare it with the original values before drawing a conclusion.
Worked example
At 20 m/s and 45° with g=9.80665 m/s², range is about 40.79 m.
Common mistake
These formulas assume launch and landing occur at the same height with no air resistance.
When does this model not apply?
Ideal classical models omit effects such as drag, relativity, extended-body geometry, material response and measurement uncertainty unless explicitly included.
How to learn with this calculator
Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.
Clear answers
Frequently asked questions
What does the Projectile motion do?
Calculate ideal launch components, flight time, maximum height and horizontal range.
How does the Projectile motion work?
The calculator applies T=2v sinθ/g; H=v²sin²θ/(2g); R=v²sin2θ/g. Horizontal velocity stays constant while gravity changes vertical velocity, allowing the motion to be separated into perpendicular components.
What can I learn from the Projectile motion?
It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.
Does MW SysArc receive or store what I enter?
No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.
How should I use the result?
Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.
Last reviewed 2026-07-14. Calculations tested 2026-07-14.