CalcLibrary

Projectile Motion Calculator

Calculate projectile range, maximum height, and flight time from initial velocity and launch angle. Assumes flat ground and no air resistance.

m/s
°
Examples

Range = 40.77 m, Max height = 10.19 m

Range
40.7747 m
Maximum Height
10.1937 m
Total Flight Time
2.8832 s
Time to Peak
1.4416 s

Low trajectory — maximises range at the cost of height.

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Examples

How It Works

Formula

R=v2sin⁡(2θ)gR = \frac{v^2 \sin(2\theta)}{g}

H=v2sin⁡2(θ)2gH = \frac{v^2 \sin^2(\theta)}{2g}

T=2vsin⁡(θ)gT = \frac{2 v \sin(\theta)}{g}

tpeak=vsin⁡(θ)gt_{peak} = \frac{v \sin(\theta)}{g}

Variables

RR

Horizontal range(m)

HH

Maximum height(m)

TT

Total flight time(s)

tpeakt_{peak}

Time to reach peak(s)

vv

Initial velocity(m/s)

θ\theta

Launch angle from horizontal(°)

gg

Gravitational acceleration (9.81)(m/s²)

Enter the initial velocity in m/s and the launch angle in degrees. The calculator computes the horizontal range, maximum height, total flight time, and time to reach peak height using standard projectile motion equations with g = 9.81 m/s².

Decompose the initial velocity into horizontal (v·cos θ) and vertical (v·sin θ) components. Gravity acts only on the vertical component, which traces a symmetric up-down parabola. The calculator solves the resulting kinematic equations in closed form: range = v²·sin(2θ)/g, peak height = v²·sin²(θ)/(2g), time to peak = v·sin(θ)/g, total flight = twice the time to peak. Air resistance is neglected.

Frequently Asked Questions

01What is projectile motion?
Projectile motion is the motion of an object thrown or projected into the air, subject only to gravitational acceleration. The path forms a parabola.
02What angle gives maximum range?
45 degrees gives the maximum range for a given initial speed on flat ground with no air resistance. Complementary angles (e.g., 30° and 60°) give the same range.
03Does air resistance affect the results?
This calculator assumes no air resistance (vacuum conditions). In reality, drag significantly reduces range and max height, especially at high speeds.
04What value of g is used?
The calculator uses g = 9.81 m/s², the standard gravitational acceleration at Earth's surface.
05What are the key formulas?
Range: R = v²sin(2θ)/g. Max height: H = v²sin²(θ)/(2g). Flight time: T = 2v·sin(θ)/g. Time to peak: t = v·sin(θ)/g.

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