Calculators
Projectile Motion Calculator
Calculate ideal projectile range, height, and flight time.
Estimate ideal projectile motion when launch and landing heights are equal and air resistance is ignored.
Horizontal range
40.788649 m
Maximum height
10.197162 m
Time of flight
2.884193 s
Initial velocity components
vx 14.142136, vy 14.142136 m/s
About This Tool
Projectile motion combines horizontal motion with vertical acceleration from gravity. This calculator estimates horizontal range, maximum height, time of flight, and the initial horizontal and vertical velocity components for the standard ideal case: the projectile launches and lands at the same height, gravity is constant, and air resistance is ignored. All calculations run locally in your browser.
How To Use It
- Enter a positive launch speed and select its unit.
- Enter a launch angle strictly between 0° and 90°, measured upward from the horizontal.
- Use standard gravity 9.80665 m/s² for a typical textbook Earth calculation, or enter another positive gravitational acceleration when the problem specifies one.
- Choose metres or feet for distance results, then interpret the outputs using the equal-height, no-drag assumptions.
Examples
20 m/s at 45°
With standard gravity, an ideal 20 m/s launch at 45° travels about 40.79 m horizontally, reaches about 10.20 m above its launch point, and stays airborne about 2.88 s.
Velocity components
At 20 m/s and 30°, the initial vertical component is 10 m/s while the horizontal component is about 17.32 m/s.
Why 45° is special
In the equal-height, no-air-resistance model with fixed launch speed, range is proportional to sin(2θ), so the maximum ideal range occurs at 45°.
Useful Notes
Ideal projectile formulas
Resolve launch speed v into vx = v cos θ and vy = v sin θ. For equal launch and landing heights, flight time is T = 2vy/g, maximum height above launch is H = vy²/(2g), and horizontal range is R = v² sin(2θ)/g.
Assumptions matter
These closed-form formulas assume constant downward gravity, level launch and landing heights, and no aerodynamic drag. Real thrown, kicked, launched, or ballistic objects can differ because of air resistance, wind, spin, shape, changing elevation, and other forces.
Angle convention
The launch angle is measured upward from the horizontal. The tool limits the angle to between 0° and 90° because the displayed range and flight-time formulas target an upward launch that later returns to the same elevation.
Gravity
Standard gravity is 9.80665 m/s². The editable gravity field makes the calculation usable for textbook problems that specify another constant gravitational acceleration without pretending one value applies everywhere.
Not a targeting model
This is an educational ideal-motion calculator. It does not account for drag, wind, rotation, terrain, geographic conditions, or a target location and should not be used as a real-world targeting or safety model.
FAQ
What launch angle gives the maximum range?
Under the calculator's equal-height, constant-gravity, no-drag assumptions, 45° maximizes horizontal range for a fixed launch speed.
Why can real range differ from this result?
Air resistance, wind, spin, object shape, launch and landing height differences, and changing environmental conditions can all make real motion differ from the ideal equations.
Is maximum height measured from the ground?
No. The displayed maximum height is above the launch elevation. Because this model assumes landing at that same elevation, it does not need a separate ground height.
Can I change gravity?
Yes. Enter a positive gravitational acceleration in m/s² when your problem specifies a different constant value.
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