Projectile Motion Calculator
Last updated: June 2026
Formula
Range and flight time are calculated from horizontal and vertical components. vx = v0 cos(angle), vy = v0 sin(angle), y = y0 + vy t - 0.5 g t^2.
About this calculator
The Projectile Motion Calculator estimates range, maximum height, time of flight, and velocity components for a launched object. It is useful for physics lessons where air resistance is ignored and gravity is treated as constant.
Projectile motion formulas
The calculator splits the initial velocity into horizontal and vertical components, solves flight time, then calculates range and maximum height.
- vx = v0 cos(theta)
- vy = v0 sin(theta)
- y = y0 + vy t - 0.5gt^2
- range = vx x time
- max height = y0 + vy^2 / 2g
How to use the projectile motion calculator
- Enter initial velocity in metres per second.
- Enter launch angle in degrees.
- Enter initial height if the projectile starts above ground level.
- Leave gravity at 9.81 m/s2 for Earth examples or change it for another body.
- Review range, maximum height, and flight time.
- Use the diagram as a simplified visual guide.
Worked examples
45-degree launch
Input: 20 m/s at 45 degrees from ground level
Calculation: Split velocity into x and y components, then solve flight time.
Result: Range is about 40.8 m.
Lower gravity
Input: Same launch with lunar gravity 1.62 m/s2
Calculation: Lower gravity increases time aloft and range.
Result: The projectile travels much farther.
Why angle matters
For same-height launch and landing without air resistance, 45 degrees gives the greatest range. Different starting heights can change the best angle.
Horizontal and vertical motion
Horizontal velocity is constant in this simple model. Vertical velocity changes because gravity accelerates the projectile downward.
Projectile model limitation
This calculator ignores air resistance, wind, spin, lift, changing gravity, and collisions. It is for educational physics examples only.
Frequently asked questions
Does this include air resistance?
No. It uses the simple no-drag projectile model.
What is g on Earth?
A common value is 9.81 m/s2.
Why split velocity into components?
Horizontal and vertical motion are solved separately.
Does initial height matter?
Yes. Starting above ground usually increases flight time and range.
Is 45 degrees always best?
Only in the simple same-height, no-drag case.
Related calculators
- speed-calculator
- acceleration-calculator
- distance-calculator
What does this mean?
This calculator is designed to help you understand the likely number before you make a decision or start an application.
Your result should be checked against official UK guidance, especially if your circumstances include dependants, exemptions, prior leave, or a complex immigration history.
Treat the figure as a planning tool rather than legal advice. Where the answer affects an application deadline or major payment, speak to an authorised adviser.
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