Calculator
Calculation history
| Time | Mode | a | b | c | Area | Perimeter | Unit |
|---|---|---|---|---|---|---|---|
| No calculations yet. Run a calculation to populate history. | |||||||
Example data table
| Example | a | b | c | Notes |
|---|---|---|---|---|
| 3-4-5 | 3 | 4 | 5 | Smallest integer triple. |
| 5-12-13 | 5 | 12 | 13 | Often used in construction layouts. |
| 8-15-17 | 8 | 15 | 17 | Scaled from 8-15-17 set. |
| 7-24-25 | 7 | 24 | 25 | Another common integer triple. |
Formula used
- c = √(a² + b²) for the hypotenuse.
- a = √(c² − b²) and b = √(c² − a²) for missing legs.
- Area of a right triangle: Area = ½ab.
- Perimeter: P = a + b + c.
How to use this calculator
- Select which side is missing: c, a, or b.
- Enter the known side values. Keep them positive numbers.
- Pick a unit label and choose decimal places for rounding.
- Click Calculate. The result appears above the form.
- Use history to compare runs, then export CSV or PDF.
Accuracy checks for field measurements
In construction and layout work, a frequent quality target is keeping diagonal checks within ±1% of the expected length. For example, if a=3 and b=4, the diagonal is c=5. A ±1% tolerance means 4.95 to 5.05 in the same unit.
Input ranges and scaling behavior
The theorem scales predictably: multiplying both legs by k multiplies the hypotenuse by k. A 5-12-13 triangle becomes 10-24-26 when doubled. This supports fast scenario testing across small parts and large site dimensions.
Rounding policy and reporting clarity
Reporting often requires consistent decimals. Using 3 decimal places gives millimetre-level detail when the unit is metres, while 0 decimals is useful for rough estimates. This tool applies the same rounding setting to sides, area, and perimeter for clean exports.
Triangle validity and strict checks
For leg calculations, the requirement c² > a² or c² > b² prevents impossible inputs. Enabling strict checks also enforces c as the largest side, which reduces data entry errors when working from tapes or drawings.
Operational metrics you can track
Each run stores timestamped results, enabling trend review across repeated measurements. If the hypotenuse fluctuates by more than 2% between runs under the same plan, it may indicate inconsistent leg inputs, unit mismatch, or movement of reference points.
Export workflow for teams
CSV export supports quick filtering and pivoting, while PDF is suitable for job packets and sign-offs. A practical practice is logging at least 3 measurements per critical corner and exporting the history as an attachment for traceability and handover.
FAQs
1) When should I solve for the hypotenuse?
Use it when you know both legs and need the diagonal distance, such as checking a rectangular layout, ramp length, or screen size from width and height.
2) Why do I get an error for leg calculations?
A leg requires c to be larger than the known leg. If c² is not greater, the square root becomes invalid, so the tool blocks the calculation.
3) What does “strict right-triangle checks” do?
It enforces the hypotenuse as the longest side and flags inputs where the known leg is equal to or longer than c. This helps catch swapped fields and unit mistakes.
4) Does the calculator work with decimals?
Yes. Enter decimals for any known side, choose your rounding precision, and the output remains consistent across the result cards, history table, and export files.
5) What units should I use?
Any unit works as long as you keep it consistent for all inputs. The unit label is printed in results and exports, including squared units for the area value.
6) How is area calculated?
For a right triangle, area is ½ab, where a and b are the perpendicular legs. The tool shows this alongside perimeter for quick geometry summaries.