Last Updated: October 20, 2025
Calculate projectile range from initial velocity and launch angle instantly with our free physics calculator supporting multiple units and real-time results for analyzing projectile motion in physics education, ballistics, and motion analysis applications.
Enter the initial velocity and launch angle values below to calculate projectile range instantly.
Use the input fields to specify initial velocity, launch angle, and other parameters for accurate calculations.
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The Projectile Range Calculator is a specialized tool that calculates the horizontal distance traveled by a projectile from its launch point to where it hits the ground. This fundamental metric is essential for understanding projectile motion in physics and has applications in ballistics, sports, and engineering.
For more information about projectile range and ballistics, visit Wikipedia: Projectile Motion and Wikipedia: Ballistics.
In physics, projectile range depends on three key factors: initial velocity, launch angle, and acceleration due to gravity. The range formula shows that maximum range occurs at a 45-degree launch angle when air resistance is negligible. This principle is fundamental in understanding how projectiles behave under the influence of gravity and is essential for maximum height calculations and time of flight analysis.
Maximum range occurs at a 45-degree launch angle when air resistance is negligible.
Whether you're studying physics, analyzing ballistics, designing sports equipment, or simply understanding the physics behind projectile motion, this calculator provides accurate, instant results with flexible unit conversions to meet your specific needs. For related calculations, explore our projectile motion calculator, trajectory calculator, maximum height calculator, time of flight calculator, and velocity calculator.
R = (v₀²sin(2θ))/g
This formula calculates the projectile range by using initial velocity, launch angle, and acceleration due to gravity.
Initial velocity (v₀) is the speed at which the projectile is launched. It's measured in units like meters per second (m/s), kilometers per hour (km/h), or feet per second (ft/s). The initial velocity determines how fast the projectile starts moving.
Launch angle (θ) is the angle at which the projectile is launched relative to the horizontal. It's measured in degrees or radians. The launch angle significantly affects the range - 45 degrees typically gives maximum range in the absence of air resistance.
Velocity conversions:
Angle conversions:
The projectile range is crucial for understanding how far a projectile will travel. The range formula shows that range is proportional to the square of initial velocity and depends on the sine of twice the launch angle. This relationship is fundamental in projectile motion analysis.
| Field/Application | Typical Range | Importance |
|---|---|---|
| Artillery Systems | 10-50 km | Critical for military operations and defense systems |
| Sports (Golf) | 200-300 m | Essential for course design and player performance |
| Water Sports | 5-50 m | Important for diving and water safety |
| Construction | 10-100 m | Critical for material handling and safety |
| Entertainment | 5-100 m | Essential for stunt coordination and safety |
| Aerospace | 100-1000 km | Critical for launch systems and orbital mechanics |
| Emergency Services | 5-100 m | Important for rescue operations and safety |
| Educational Physics | 1-50 m | Essential for understanding fundamental motion principles |
Given:
Step 1: Calculate sin(2θ)
sin(2 × 30°) = sin(60°) = 0.866
Step 2: Calculate v₀²
20² = 400 m²/s²
Step 3: Apply the range formula
R = (400 × 0.866) / 9.81 = 35.3 m
Final Answer
35.3 meters
Projectile range
Given:
Step 1: Calculate sin(2θ)
sin(2 × 45°) = sin(90°) = 1
Step 2: Calculate v₀²
25² = 625 m²/s²
Step 3: Apply the range formula
R = (625 × 1) / 9.81 = 63.7 m
Final Answer
63.7 meters
Maximum projectile range
Given:
Step 1: Convert velocity to m/s
60 km/h × (1000 m/km) × (1 h/3600 s) = 16.67 m/s
Step 2: Calculate sin(2θ)
sin(2 × 60°) = sin(120°) = 0.866
Step 3: Calculate v₀²
16.67² = 277.8 m²/s²
Step 4: Apply the range formula
R = (277.8 × 0.866) / 9.81 = 24.5 m
Final Answer
24.5 meters
Projectile range
💡 Did you know? The range formula shows that doubling the initial velocity quadruples the range — that's why powerful projectiles travel much farther!
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