Worked example: Pythagorean Theorem Calculator
3-4-5. This fixed reference example shows one complete scenario; the interactive results above use your current inputs.
View the example inputs
- Perpendicular leg a
- 3 length units
- Perpendicular leg b
- 4 same units
| Calculated quantity | Example result |
|---|---|
| Hypotenuse | 5 |
| Area | 6 |
| Perimeter | 12 |
| Angle opposite a | 36.8699 ° |
| Angle opposite b | 53.1301 ° |
Choosing dimensions for a geometry calculation
Identify the shape and the meaning of each length
A geometric formula depends on the shape and the role of each dimension. A radius is half a diameter, a semi-axis is half an ellipse’s full axis, and a perpendicular height is different from a sloped side. Confirm the labels before entering dimensions.
Use one consistent length unit unless the form provides a conversion selector. Area is expressed in square units and volume in cubic units. Multiplying every length by a factor of two multiplies an area by four and a volume by eight.
Check that the measurements describe a possible shape
A set of positive numbers does not necessarily form a triangle, and a non-square matrix does not have a determinant. Each operation has domain and dimension requirements, which the calculator checks where applicable.
A geometric quantity is not a structural design. Material waste, packing, thickness, loading and construction tolerances require additional inputs or a separate estimator. The worked example shows the idealized formula without adding those assumptions.
Formula and calculation method
c=sqrt(a²+b²); area=ab/2. Both inputs are legs, not a hypotenuse.
Reference Sources
Frequently asked questions
How does this calculator work?
c=sqrt(a²+b²); area=ab/2. Both inputs are legs, not a hypotenuse.
What assumptions should I check?
Check the units and definitions shown beside each input. Results use the values you enter.
Can I save or print this calculation?
Use Copy link with inputs to reproduce the scenario, Download results for a text record, or Print. Where a schedule is shown, its CSV download includes every row.