How to use the projectile range calculator
Prepare the values for this calculation
Calculate ideal level-ground projectile range without air resistance. Use the formula below to check that it answers your question. Read the input units before transferring figures from a statement, measurement or dataset.
Enter and check each input
- Launch speed (m/s): enter a value at least 0. Use the unit named in the label or selected above. Do not leave this required field blank.
- Launch angle (degrees): enter a value at least 0 and no more than 90. Use the unit named in the label or selected above. Do not leave this required field blank.
- Gravitational acceleration (m/s²): enter a value at least 1e-06. Use the unit named in the label or selected above. Do not leave this required field blank.
The input table gives a complete example. Keep units and time periods consistent across related fields.
Calculate and resolve any input error
Choose Calculate after entering the values. Changes also update the answer after a short pause. If an error appears, follow its message, correct the field and calculate again. Reset restores the example values.
Interpret the answer
Check Ideal range first. With the unchanged example inputs, it is 40.7886485191 m. Interpret it using the formula and assumptions on this page.
Compare and keep a useful result
For a controlled comparison, keep every other example input unchanged and change Launch speed (m/s) from 20 to 22. The resulting Ideal range is 49.3542647081 m. This illustrates the equation’s response to that input, rather than a forecast of real events.
Read the chart’s axis labels and data table. A scenario curve changes one stated input while holding the others fixed; it does not add external observations. Use Download graph to save an available chart as a PNG.
Use Copy result or Download CSV to keep the answer. Share tool shares the page address without placing your input values in the URL. Recheck inputs and assumptions before using the result for a decision.
Projectile Range Calculator formula
R=v² sin(2θ)/g for equal launch and landing elevations.
Inputs and units
| Input | Format / range | Example |
|---|---|---|
| Launch speed (m/s) | minimum 0 | 20 |
| Launch angle (degrees) | minimum 0; maximum 90 | 45 |
| Gravitational acceleration (m/s²) | minimum 1e-06 | 9.80665 |
Worked example
Using the example inputs above, the ideal range is 40.7886485191 m.
- Ideal range
- 40.7886485191 m
Results and assumptions
Idealized vacuum result for equal launch and landing elevations.
Fix an input or unexpected result
Launch speed (m/s) is required. Enter launch speed (m/s) using the format and bounds in the input table. Zero and an empty field are different: use zero only if it is allowed and represents your data.
If your answer differs from the example, choose Reset and compare every field, including selected units and options. Check percentage versus decimal entry and whether values describe the same period. Round only the final displayed answer when reproducing the formula.
If a discrepancy remains, report the calculator issue with the page address, non-sensitive example inputs, actual result, expected result and a reference for your calculation.