Construction geometry
Right triangle lengths and angles
Solve a right triangle from two legs, a hypotenuse and leg, or a horizontal leg and angle.
Your inputs
Complete the fields for your selected method. Zero means intentionally zero, not unknown. Currency selection labels amounts; it does not convert exchange rates.
How this calculation works
two legs: hypotenuse = sqrt(base² + rise²); angle = atan(rise / base); base and angle: rise = base × tan(angle)
Measurement arithmetic for the stated ideal shape. Verify dimensions and assumptions at the site. No structural sizing, code compliance, safe load, stair approval, accessibility certification or boundary survey is supplied. Exactly one angle is assumed to be 90 degrees. The entered angle is measured between the horizontal leg and hypotenuse, in degrees. The resulting lengths are geometry only, not approved rafter, ramp or support dimensions.
What information do I need?
Use records for the same job, equipment or accounting period. Only the fields for your selected entry method are required. An unknown amount is not zero.
Input definitions and where to find them
- Known dimensions: Use a measured value or an explicit assumption for the stated geometry; check the selected entry method and units.
- Horizontal leg (ft): Measure the stated distance and select its unit. Feet, inches and meters are supported. A perpendicular height is not a sloping length.
- Perpendicular rise (ft): Measure the stated distance and select its unit. Feet, inches and meters are supported. A perpendicular height is not a sloping length. Used with: Two perpendicular legs.
- Hypotenuse (ft): Measure the stated distance and select its unit. Feet, inches and meters are supported. A perpendicular height is not a sloping length. Used with: Hypotenuse and horizontal leg.
- Angle above the horizontal leg (degrees): Use a measured value or an explicit assumption for the stated geometry; check the selected entry method and units. Used with: Horizontal leg and angle above it.
Use the Where to find this value controls beside the inputs for available work-it-out helpers. Estimates remain your assumptions; a helper does not verify the source figures.
Worked example
Example amounts use US dollars (USD).
Example answer: Hypotenuse is 5.0000 ft for the illustrative inputs below.
Example inputs
- Known dimensions: Two perpendicular legs
- Horizontal leg: 3.00 ft
- Perpendicular rise: 4.00 ft
- Hypotenuse
- 5.0000 ft
- Horizontal leg
- 3.0000 ft
- Perpendicular rise
- 4.0000 ft
- Angle above horizontal
- 53.1301 degrees
- Other acute angle
- 36.8699 degrees
- Triangle area
- 6.0000 ft²
These illustrative values are not recommended rates or industry averages. Replace every example input with your own figures.
Use the result well
Solve a right triangle from two legs, a hypotenuse and leg, or a horizontal leg and angle.
Keep inputs on the same scope and time basis. Calculations retain precision internally; displayed values generally round to two decimal places, with extra precision for very small values and whole-unit rounding where required. Economic comparisons describe your supplied assumptions and do not guarantee future results.
This tool provides business arithmetic. It does not approve engineering designs, establish legal or tax treatment, select equipment or certify safe operating conditions.