Projectile Range Calculator
Enter initial speed and launch angle to compute the horizontal range R = v₀²·sin(2θ)/g of a projectile.
Input Data
Results
At a glance:The range of a projectile (launch and landing at the same height, no drag) is R = v₀²·sin(2θ)/g, derived from the flight time T = 2v₀·sinθ/g times the horizontal speed v₀·cosθ. It is symmetric about 45°: angles θ and 90°−θ give the same range. Range scales with v₀² and is maximized at θ=45° (sin2θ=1). Air resistance reduces the real range, especially at high speed. This tool returns R from v₀, θ and g.
Formula
R = v₀²·sin(2θ)/g
$$R = \frac{v_0^2 \sin(2\theta)}{g}$$How to Use
- Enter initial speed v₀ (m/s).
- Enter launch angle θ (°) and gravity g.
- The calculator returns the range R.
Case Studies
Javelin throw
v₀ = 28 m/s, θ = 45°, g = 9.81.
R = 784×1/9.81 ≈ 80 m.
Ideal range (no drag).
FAQ
Why is 45° optimal?
Range ∝ sin(2θ), which is maximum (1) at 2θ=90°, i.e. θ=45°, balancing horizontal speed and flight time.
Are 30° and 60° equivalent?
Yes — sin(60°)=sin(120°), so a 30° and 60° launch (same v₀) give the same range, just different heights/times.
Related Tools
References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.