When to use this calculator
A 45° launch maximises range only within this ideal equal-height model. Wind, drag and height differences change the result.
Explore the motion & kinematics calculators for other questions in this topic. For a related calculation, use the Reaction Distance Calculator: Find distance travelled at constant speed during a reaction delay.
PUTTING IT INTO PRACTICE
Projectile Range: a worked example
The values below are an illustrative example, not a recommendation. Replace them with measurements or assumptions that match your question.
| Input | Example value |
|---|---|
| Launch speed (m/s) | 10 |
| Launch angle (degrees) | 45 |
| Gravity (m/s²) | 10 |
| Result | 10 m |
- Check the input labels and enter the example values above.
- Apply the relationship: Range = speed² × sin(2 × angle)/gravity.
- The result is 10 m, rounded for display.
How to interpret your result
Assumes equal launch and landing heights, constant gravity and no air resistance.
Choose a reference direction before using signed velocities. Constant-acceleration models do not capture variable braking or drag. Projectile tools explicitly state launch and landing assumptions.
Frequently asked questions
Are displacement and distance interchangeable?
No. Displacement is the signed or directed change in position; distance counts the length of the path travelled.
When is the projectile range calculator useful?
A 45° launch maximises range only within this ideal equal-height model. Wind, drag and height differences change the result.
How do I use the projectile range calculator?
Enter launch speed (m/s), launch angle (degrees), gravity (m/s²). The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
Range = speed² × sin(2 × angle)/gravity.
What should I check before using the result?
Assumes equal launch and landing heights, constant gravity and no air resistance.
How are results rounded?
Scalar numbers display up to six decimal places, with scientific notation for very large or small values. Text, fraction, date and schedule outputs use the format described on the tool. Intermediate calculations use JavaScript floating-point arithmetic. Keep sensible precision for your measurements.
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