Free · Mathematical relations and geometry

Right-Angle Slant and Hypotenuse Measures

Find a cone generator, right-triangle hypotenuse or right-angle cross-section diagonal from perpendicular lengths.

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

A cone with radius 3 and perpendicular height 4 has slant height 5. The same 3–4–5 relation applies to a right triangle.

l² = h² + b²; cone b is its base radius

Worked example

Enter these known values and leave the other values blank.

Shape type
1
Height (h)
4 m
Base radius (r)
3 m
Slant height (l)
5 m

Assumptions and limitations

  • A right circular cone uses perpendicular height and radius, giving the sloping generator.
  • The prism option uses a right-angled cross section with the full horizontal leg. Its fields retain internal pyramid names but do not calculate a square-pyramid face slant from a full base edge.
  • The third mode is a right triangle. Lengths are positive; the hypotenuse must exceed either leg.
  • Inverse calculations select the positive square root.

Common questions

How can I solve for a missing quantity?

Leave the unknown control empty and enter the quantities needed by the selected relation. Read the assumptions for any branch or domain restrictions.

How should I interpret the worked example?

It is an exact mathematical model with independently checked numbers. Display rounding does not change the values used for subsequent calculations.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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