Science calculator
Projectile Motion Calculator
Calculate range, height, and flight time of a projectile.
About the projectile motion calculator
The projectile motion calculator calculates range, maximum height, and flight time for a launched projectile.
How to use this calculator
- 1
Enter initial velocity
Enter the launch speed in m/s.
- 2
Enter launch angle
Enter the angle above horizontal in degrees.
- 3
Enter initial height
Enter the launch height above ground (0 for ground level).
How the calculation works
Range = v²sin2θ/g. Max height = (vsinθ)²/2g. Time = (vsinθ + √((vsinθ)²+2gh))/g.
Example: 20 m/s at 45° from 1m: range≈42m, max≈11m, time≈2.9s.
Understanding scientific constants
Key constants used: g = 9.81 m/s² (Earth gravity), c = 299,792,458 m/s (speed of light), G = 6.674×10⁻¹¹ N·m²/kg² (gravitational constant), h = 6.626×10⁻³⁴ J·s (Planck's constant), R = 8.314 J/(mol·K) (ideal gas constant). Results assume ideal conditions — real-world measurements may vary.
Ideal vs. real-world conditions
Most physics calculators assume ideal conditions: no air resistance, perfect vacuums, uniform gravity. Real-world results will differ due to friction, air resistance, temperature variations, and measurement uncertainty. Use these tools for learning and estimation, not precision engineering.
Important limitations
This tool provides a mathematical estimate based only on the values entered. It does not account for regulations, taxes, lender fees, market conditions, or individual circumstances. Results are for planning purposes only — consult a qualified professional for regulated, medical, financial, or construction decisions.
Frequently asked questions about projectile motion calculator
How accurate is the projectile calculator?+
The calculation follows the displayed formula and retains full numeric precision before formatting the result.
Can I use the result professionally?+
Use it as a planning estimate. Confirm regulated, medical, financial, or construction decisions with a qualified professional.