Triangle & Angle Calculator
Enter a run and a rise to get the slope length and angle. Solves right, isosceles and general triangles, and arcs
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Enter the run and rise of a right triangle to get the hypotenuse and angle, or solve isosceles triangles, any triangle and circular arcs. Use it for ramps, roof pitch, stairs or the radius of an arch.
How to use
- Choose the "Right triangle", "Isosceles", "Any triangle" or "Arc" tab.
- Fill in only the values you know: two values, or three including a side on "Any triangle". The empty fields show the calculated values.
- The drawing follows the true proportions of your values, and area, perimeter, slope and heights appear below. "Show formulas" lists the equations used.
- Under "Units and display", set the length unit, angle unit and decimal places; "Copy results" copies everything.
How it works
- Right triangles use c = √(a² + b²) and A = arctan(b ÷ a). Any triangle uses the laws of sines and cosines, and Heron's formula for the area.
- If two sides and an angle not between them (SSA) fit two triangles, both are shown. Values that cannot form a triangle get an explanation.
- The length unit is only a label and does not convert values.
Questions and answers
- How do I find the hypotenuse from the base and height?
- c = √(a² + b²). A run of 4 and a rise of 3 give a hypotenuse of √(16 + 9) = 5 and an angle A of about 36.87°.
- How do I convert a slope percentage to an angle?
- Slope = rise ÷ run × 100 and angle = arctan(rise ÷ run). A run of 4 and a rise of 3 give a 75% slope and about 36.87°.
- Can I find the angles from three sides?
- Yes. Enter them under "Any triangle"; the law of cosines gives all three angles. The longest side must be shorter than the other two together.
- How do I find a radius from a chord and arc height?
- Enter both on the "Arc" tab; it uses r = c² ÷ 8h + h ÷ 2. A chord of 100 and an arc height of 10 give a radius of 130.