Projectile Motion Calculator

Find horizontal and vertical launch components, time of flight, range, maximum height, and impact speed for ideal motion without air resistance.

Launch speed

Launch angledegrees above horizontal

Initial height

Gravitym/s²

—Time of flight

—Horizontal range

—Maximum height

—Impact speed

—Ideal projectile, constant gravity, no air resistance.

These are idealized classical-physics calculations. Real systems can differ because of air resistance, friction, deformation, measurement uncertainty, non-constant forces, or other effects not included in the selected model.

Physics model preflight

Check the governing model before trusting the number

2D projectile, constant gravity, no drag

x = v₀cosθ·t · y = h₀ + v₀sinθ·t − ½gt²

Reading the current native inputs…

Initial speed/height are non-negative and g positive. Air resistance is excluded. This is an idealized educational model: unit consistency and valid inputs do not guarantee that omitted effects are negligible in a real system.

Trajectory & target-speed audit

Cross-check the no-drag trajectory and solve required launch speed for a target range at the selected angle.

Physics evidence

Target range (m)

Metric	Value	Meaning

Practical guide and verification

State the model first

Basic projectile equations usually assume constant gravitational acceleration, no air resistance and a flat reference frame. Those assumptions are useful for textbook problems but can diverge from real motion when drag, wind or large distances matter.

Separate horizontal and vertical motion

Under the ideal model, horizontal velocity remains constant while vertical velocity changes because of gravity. Keeping those components separate helps avoid mixing angle, speed and displacement formulas.

Common mistake

Check whether the launch and landing heights are equal before using a symmetric range or flight-time shortcut. A formula derived for equal heights can give the wrong result when the target is above or below the launch point.

State the model before trusting the number

Classical formulas are only as good as their assumptions and units. Air resistance, damping, deformation, non-constant forces and measurement uncertainty are not silently invented when the selected model does not include them.

Governing physics model

x = v₀cosθ·t · y = h₀ + v₀sinθ·t − ½gt² — 2D projectile, constant gravity, no drag.

How to verify the result

Check horizontal range as vₓ·t and maximum height from h₀ + vᵧ²/(2g). With h₀ = 0 and no drag, 45° maximizes range for a fixed speed.

Domain and assumption boundary

Initial speed/height are non-negative and g positive. Air resistance is excluded. The calculator does not silently add drag, damping, deformation, varying fields, relativistic effects, measurement uncertainty, or geometry that the selected model does not contain.