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Right Cone Slant Length, Base Angle and Half-Apex Angle

Calculate right cone slant length, base angle and half-apex angle with converted units, positive geometric inverses and explicit model limits.

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

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For radius 3 cm and height 4 cm, slant length is 5 cm, base angle is approximately 53.1301° and half-apex angle is approximately 36.8699°.

s² = r² + h²; α = asin(h/s); β = asin(r/s); α + β = 90°

Enter these known values and leave the other values blank.

The two angles belong to the right-triangle cross-section between axis, radius and slant. β is half the full apex angle; the full apex angle is 2β. Both angles must lie strictly between 0° and 90°.
Measurements must describe the same shape. Clear a quantity you want to infer instead of supplying conflicting measurements. Unit selectors are converted before the geometric relationships are applied.
Calculations use 64 significant digits with full-precision π; result formatting rounds the displayed value separately. These are ideal geometric models, without material allowances or measurement uncertainty.

No. It is the angle between the axis and one slant edge. Double β for the complete apex angle in an axial cross-section.

Require real, positive geometric inverses and the stated shape domain before displaying derived results.