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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.
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.
This calculator uses the classical projectile motion formula to determine how far the object will travel:
The standard formula (assuming launch and landing height are equal and no air resistance) is:
Range = (v² × sin(2θ)) ÷ g
Where:
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.
For more advanced users, we also provide support for different units and input scenarios.
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.
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.
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!
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.
You use the formula:
Range = (v² × sin(2θ)) ÷ g, where v is velocity, θ is angle, and g is gravity.
Just enter the velocity, angle, and gravity into our calculator. It will show how far the projectile travels.
Use the formula with θ = 75°. The range will be shorter than at 45°, assuming same speed.
Yes! It works for any object launched into projectile motion — as long as you know the speed and angle.