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Projectile Range Calculator

Accurately calculate projectile range with our free online calculator. Enter velocity, angle & gravity to get instant results with formula and steps.

Understanding how far a projectile will travel can be both exciting and essential for students, engineers, hunters, archers, and physics enthusiasts. That's why we developed this easy-to-use Projectile Range Calculator. Whether you're firing a baseball, an arrow, or launching a cannonball in a physics experiment, this tool helps you calculate the projectile’s range instantly and accurately using physics-based formulas.

Let’s break it down and show how it works with real-world values, formulas, and frequently asked questions.

What Is Projectile Range?

Projectile range is the horizontal distance a projectile travels from its launch point to where it lands. It depends on three key factors: initial velocity, launch angle, and gravitational acceleration.

The range is largest when the object is launched at a 45-degree angle in a vacuum (no air resistance). For angles higher or lower than 45°, the range gets shorter under the same velocity.

How the Projectile Range Calculator Works

This calculator uses the classical projectile motion formula to determine how far the object will travel:

Range of a Projectile Formula

The standard formula (assuming launch and landing height are equal and no air resistance) is:

Range = (v² × sin(2θ)) ÷ g

Where:

  • v is the initial velocity (m/s or mph)
  • θ is the launch angle (in degrees or radians)
  • g is the gravitational acceleration (usually 9.81 m/s² on Earth)

For example, if a ball is thrown at 30 m/s at a 45-degree angle:

Range = (30² × sin(90)) ÷ 9.81 = 900 ÷ 9.81 ≈ 91.74 meters

You can also convert this into feet, kilometers, or miles instantly using our tool.

How to Use the Projectile Range Calculator

  1. Enter the velocity – in m/s, km/h, mph, or ft/s
  2. Set the angle – in degrees or radians
  3. Choose gravity – use Earth’s gravity (9.81) or adjust it for Mars, Moon, etc.
  4. Click Calculate – the calculator will show:
    - The total horizontal range
    - Maximum height
    - Total time of flight
    - Distance in meters, feet, km, and miles

For more advanced users, we also provide support for different units and input scenarios.

Range of a Projectile from Height

If the projectile is launched from a height above the ground, the basic formula changes. Here’s the extended version:

Range = v × cos(θ) × [v × sin(θ) + √(v² × sin²(θ) + 2gh)] ÷ g

Where h is the launch height.

This formula accounts for the extra time the projectile is in the air due to the starting elevation.

What About Air Resistance?

This calculator currently provides results assuming no air resistance, which is ideal for basic physics applications and learning. However, if you want to calculate the range with air resistance, it becomes much more complex and depends on factors like drag coefficient, shape, and mass of the projectile.

We are working on developing a future version of the calculator that includes projectile motion with air drag.

Example: 120 MPH at 31.5 Degrees

Let’s say you want to calculate how far a ball travels if thrown at 120 mph with a 31.5° angle.

First, convert velocity:

120 mph = 53.64 m/s

Then apply the formula:

Range = (53.64² × sin(2 × 31.5°)) ÷ 9.81 ≈ 138.86 meters

You can instantly do this with our calculator – no need for manual math!

Final Verdict

Our Projectile Range Calculator is built for anyone who needs quick and accurate calculations – whether for a class assignment, physics problem, archery setup, or just curiosity. The interface is simple, the results are accurate, and the formulas are 100% based on classical physics.

Frequently Asked Questions

How do you find the range of a projectile?

You use the formula:

Range = (v² × sin(2θ)) ÷ g, where v is velocity, θ is angle, and g is gravity.

How to find how far a projectile goes?

Just enter the velocity, angle, and gravity into our calculator. It will show how far the projectile travels.

What is the range of a projectile fired at 75 degrees?

Use the formula with θ = 75°. The range will be shorter than at 45°, assuming same speed.

Can this calculator be used for arrows or cannonballs?

Yes! It works for any object launched into projectile motion — as long as you know the speed and angle.