Updated Physics & Engineering Tool

Projectile Range Calculator

Compute horizontal range, time of flight, maximum height and impact speed for projectiles in idealized motion. Switch between flat ground, launch height, trajectory details and optimal angle modes with flexible units and gravity presets.

Range & max height Time of flight Gravity presets Optimal launch angle

Multi-Mode Projectile Range Calculator

Use the tabs to analyze projectile motion on level ground, include launch height, inspect full trajectory details or explore how launch angle affects range. Choose units and gravity presets that match your scenario, from Earth to the Moon.

Use presets for Earth, Moon, Mars or Jupiter, or enter a custom value.
Results still use SI internally; distances are reported in your chosen unit.

This mode assumes the projectile lands at the same vertical level from which it was launched (no launch height). Air resistance, spin and wind are ignored.

Interpreted in the current distance output unit (meters or feet).

This mode includes an initial launch height h0 above the landing level. The vertical position follows y(t) = h0 + v sin(θ)t − ½gt², and the calculator finds when the projectile returns to y = 0.

Get a full breakdown of the projectile’s motion, including horizontal and vertical components, time to peak, total flight time, range, maximum height, impact speed and impact angle.

This mode assumes flat ground and no launch height. In ideal projectile motion without air resistance, the maximum range occurs at a launch angle of 45°, but the table also shows how range changes for several angles.

Gravity affects every aspect of projectile motion. Changing the value of g in the global settings above updates all tabs. Use these presets or enter your own value for experiments.

Common Gravity Values (m/s²)

Environment Approximate g (m/s²) Notes
Earth (sea level) 9.80665 Standard gravity used in most physics problems and engineering calculations.
Moon 1.62 About 1/6 of Earth's gravity. Projectiles travel higher and stay in the air longer.
Mars 3.71 About 38% of Earth's gravity. Useful for planetary science examples.
Jupiter (cloud tops) 24.79 More than twice Earth's gravity, dramatically reducing range and height.
Custom Your choice Enter any positive value for g in the global field to model other worlds or hypothetical scenarios.

For most classroom problems on Earth, using g = 9.8 m/s² is sufficient. For more precise work, the standard value 9.80665 m/s² is often used.

Projectile Range Calculator – Ideal 2D Projectile Motion

Projectile motion is a classic topic in physics: an object is launched with some initial speed and angle under the influence of gravity alone. This Projectile Range Calculator lets you explore that motion interactively, computing horizontal range, time of flight, maximum height and impact speed for a wide range of scenarios.

The calculator assumes ideal projectile motion with no air resistance, constant gravity and a flat landing surface. In the launch-height modes, an initial height above the landing level is included in the equations. These assumptions match most textbook examples and many engineering approximations.

Core Equations of Projectile Motion

The motion is typically decomposed into horizontal and vertical components. With launch speed v, angle θ and gravity g:

  • Horizontal velocity: vx = v cos(θ)
  • Initial vertical velocity: vy0 = v sin(θ)
  • Horizontal position: x(t) = vx t
  • Vertical position without launch height: y(t) = vy0 t − ½ g t²

For a projectile that lands at the same height from which it was launched (flat ground), the time of flight T and horizontal range R are:

  • Time of flight: T = 2v sin(θ) / g
  • Horizontal range: R = v² sin(2θ) / g
  • Maximum height: Hmax = v² sin²(θ) / (2g)

Including Launch Height h₀

If the projectile is launched from a height h0 above the landing level, the vertical position becomes:

y(t) = h0 + v sin(θ) t − ½ g t²

Solving y(t) = 0 for the time when it hits the ground gives:

Tflight = (v sin(θ) + √[(v sin(θ))² + 2gh0]) / g

The range is then R = v cos(θ) · Tflight, and the maximum height is h0 plus the additional rise due to the vertical component of the velocity.

How the Multi-Mode Projectile Calculator Works

The calculator is organized into four main computational modes plus a gravity reference tab:

  • Flat Ground Range: Level launch and landing heights, ideal for pure textbook problems.
  • Range with Launch Height: Adds an initial elevation above the landing level.
  • Trajectory Details: Provides a full breakdown of horizontal/vertical components, times and speeds.
  • Optimal Angle: Illustrates how launch angle affects range and highlights the maximum range angle.
  • Gravity Info: Shows common gravity values and explains how to use presets and custom values.

Unit and Gravity Options

Real projects and homework problems often use different unit systems. To keep things flexible, the calculator:

  • Accepts speed in m/s, ft/s, km/h or mph.
  • Reports distances in either meters or feet.
  • Uses gravity in m/s² with presets for Earth, Moon, Mars and Jupiter.
  • Performs all internal calculations in SI units and converts results to your chosen units at the end.

When Does the 45° Rule Apply?

A common rule of thumb is that a 45° launch angle maximizes range. This is true when:

  • The projectile is launched and lands at the same height.
  • There is no air resistance.
  • Gravity is constant.

When the launch height is non-zero, or when air resistance is significant, the best angle shifts away from 45°. The optimal-angle tab focuses on the ideal flat-ground case and shows how range changes for several sample angles.

How to Use the Projectile Range Calculator Effectively

  • Start in the Flat Ground Range tab to understand basic relationships.
  • Switch to Range with Launch Height when your starting point is above the landing level.
  • Use the Trajectory Details tab to see components and impact properties for deeper analysis.
  • Experiment with the Optimal Angle tab to see how sensitive range is to angle changes.
  • Use the Gravity presets to explore how motion differs on the Moon, Mars or Jupiter.

For classroom work, this calculator helps visualize formulas and double-check hand calculations. For engineering, sports and basic planning, it offers a quick way to obtain idealized estimates before considering more complex effects like drag and spin.

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Projectile Motion FAQs

Frequently Asked Questions About Projectile Range

Clear answers to common questions about range, height and time of flight.

Ideal projectile motion without air resistance leads to clean analytical formulas and fast calculations. Once drag is included, the equations become more complex and often require numerical methods. For education and quick estimates, the idealized model is usually sufficient and matches most textbook examples.

Yes. At 90° the range becomes essentially zero and the motion is purely vertical; the calculator focuses on time of flight and maximum height in that case. At very low angles, the range stays finite but maximum height is small. The formulas smoothly handle intermediate angles as well.

The calculator checks for non-positive gravity values and prevents the calculation, since the formulas are only meaningful when gravity is positive. Make sure to use realistic values for g, such as 9.8 m/s² on Earth or the presets for other celestial bodies.

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