projectile motion formulas and interpretation
Projectile motion separates horizontal constant velocity from vertical acceleration due to gravity.
The calculator supports launch height, angle, speed, gravity, and metric or imperial units.
How to use the projectile motion calculator
- Choose a model: Select the relationship matching the problem.
- Choose the unknown: Select the quantity to calculate.
- Enter values: Enter all known values with matching units and signs.
- Calculate: Review the result, formula, units, and direction.
Formula and variables
Horizontal range equals constant horizontal velocity multiplied by total flight time.
R = v₀cos(θ)t- R — Range
- Horizontal travel distance (m)
- v₀ — Launch speed
- Initial speed (m/s)
- θ — Launch angle
- Angle above horizontal (degrees)
- t — Flight time
- Time until landing height (s)
45-degree launch
A projectile launches at 50 m/s from ground level at 45 degrees.
- Speed
- 50 m/s
- Angle
- 45°
- Gravity
- 9.81 m/s²
- t ≈ 7.21 s
- R ≈ 254.8 m
Result: Ideal range is about 255 m.
Air resistance and wind are excluded.
Understanding your results
Interpreting the result
The ideal model assumes constant gravity and no aerodynamic drag.
Assumptions
- The selected equation represents the physical system.
- Inputs use a consistent reference direction.
- Values are converted through coherent SI units.
Limitations
- Vector components must be resolved along a common axis.
- External forces or energy losses are not added automatically.
- Results depend on the accuracy of entered measurements.
Common mistakes
- Mixing incompatible units.
- Dropping negative signs that represent direction.
- Using weight where mass is required.
- Entering a zero divisor.
Practical use cases
Physics problems
Check classroom, laboratory, and mechanics calculations.
Practical estimates
Estimate motion, forces, and energy for real systems.
Frequently asked questions
Can a result be negative?
Yes. For directional quantities, the sign indicates direction relative to the chosen positive axis.
Should I use SI units?
The interface can convert supported units, while the formulas are evaluated through coherent SI units.
Sources and review
- SI Brochure, 9th edition — BIPM. Accessed 2026-07-11.
- Special Publication 811 — NIST. Accessed 2026-07-11.
Reviewed 2026-07-11.