Two-dimensional motion tool

Projectile Motion Calculator

Calculate range, maximum height, flight time, and velocity components from launch speed, launch angle, and gravity.

Enter launch conditions

Calculate projectile motion

Free tool

Enter the launch speed of the projectile.

Use an angle greater than 0° and less than 90°.

Standard Earth gravity is 9.81 m/s².

Try an example:

Your result will appear here

Enter velocity, launch angle, and gravity, then select calculate.

Calculator guide

How this calculator works

Projectile Motion Calculator analyzes the two-dimensional movement of objects launched through the air. It helps physics students, engineers, athletes, and laboratory users calculate range, maximum height, flight time, and trajectory using velocity, angle, and gravitational acceleration.

Formula explanation

Projectile motion calculations analyze objects moving under gravity with horizontal and vertical velocity components.

Formula

Range = v₀² × sin(2θ) ÷ g, Maximum Height = v₀² × sin²(θ) ÷ 2g, Flight Time = 2v₀sin(θ) ÷ g

Worked example

Example: Launch angle and initial velocity determine projectile range and flight time.

Assumptions

  • Air resistance is ignored in the ideal projectile model.
  • Gravity remains constant throughout the motion.
  • Launch and landing conditions follow standard projectile assumptions.
  • Input values use compatible scientific units.

Examples

  • Example: Calculate projectile range when launch velocity and angle are known.
  • Example: Engineers and scientists analyze trajectories of moving objects using projectile motion equations.

Common mistakes

  • Ignoring gravitational acceleration.
  • Using incorrect angle units.
  • Treating horizontal and vertical motion the same.

Variables

  • Initial velocity
  • Launch angle
  • Flight time
  • Horizontal displacement
  • Vertical displacement
  • Maximum height
  • Gravitational acceleration
  • Measurement units

Limitations

  • Results assume ideal projectile motion without aerodynamic effects.
  • Complex trajectories may require advanced simulation methods.

Scientific references

  • OpenStax University Physics: Projectile Motion
  • NIST physical constants and measurements
  • Classical mechanics principles

Content review

Reviewed by: ScienceCalcHub Physics Review Team | Last reviewed: 2026-08-30

Applications

  • Physics education
  • Projectile trajectory analysis
  • Sports science calculations
  • Engineering simulations
  • Ballistics and motion studies
  • Laboratory experiments

Frequently asked questions

How is projectile range calculated?

Projectile range is calculated using initial velocity, launch angle, and gravitational acceleration with the equation R = v₀²sin(2θ) ÷ g.

What factors affect projectile motion?

Projectile motion depends on initial velocity, launch angle, gravitational acceleration, and external forces such as air resistance.

Why are horizontal and vertical motions separated?

Horizontal and vertical motions are analyzed separately because horizontal velocity remains constant while gravity changes vertical velocity.

Does air resistance affect projectile motion?

Yes. Real projectiles experience air resistance, but ideal calculations ignore drag to simplify physics analysis.

Accuracy and transparency

Created and maintained by our editorial team

This physics calculator is maintained by the ScienceCalcHub Editorial Team. Its calculation logic is tested with representative inputs, while the supporting guidance is checked for formula clarity, units, assumptions, and common mistakes.

Written by
ScienceCalcHub Editorial Team
Reviewed by
ScienceCalcHub Scientific Review Team
Review standard
Formula accuracy, units, examples, and educational clarity

Learn more about our formula-review and correction process, explore our calculation methodology, or view our scientific references.

  • Calculation logic tested
  • Variables and units explained
  • Assumptions stated clearly
  • Corrections handled transparently

Physics formula

How projectile motion is calculated

Projectile motion combines constant horizontal velocity with vertical acceleration caused by gravity. The launch velocity is resolved into horizontal and vertical components before range, height, and flight time are calculated.

The standard model assumes negligible air resistance and equal launch and landing heights. Real-world results can differ when drag, wind, or elevation changes are significant.

Worked example

Projectile motion example calculation

Suppose an object is launched with a speed of 20 m/s at an angle of 45° with gravity of 9.8 m/s². The horizontal and vertical velocity components are calculated first, then used to find range, maximum height, and flight time.

This example demonstrates how the calculator applies projectile motion equations under ideal conditions without air resistance.

Study vertical motion independently with the Free Fall Calculator.

Calculate changes in velocity with the Acceleration Calculator.

Questions and answers

Calculator FAQ

How is projectile range calculated?

Projectile range is calculated using initial velocity, launch angle, and gravitational acceleration with the equation R = v₀²sin(2θ) ÷ g.

What factors affect projectile motion?

Projectile motion depends on initial velocity, launch angle, gravitational acceleration, and external forces such as air resistance.

Why are horizontal and vertical motions separated?

Horizontal and vertical motions are analyzed separately because horizontal velocity remains constant while gravity changes vertical velocity.

Does air resistance affect projectile motion?

Yes. Real projectiles experience air resistance, but ideal calculations ignore drag to simplify physics analysis.