Formulas, without the guesswork.
Choose a relationship from the measurements you know. The variable names below belong to each calculator; a letter can have a different role in another method. π is evaluated using the browser’s full numerical constant, rather than replacing it with 3.14.
Radius and vertical height
Inputs: Radius r (length units); Vertical height h (length units).
Radius and slant height
Inputs: Radius r (length units); Slant height l (length units).
Volume and radius
Inputs: Volume V (cubic units); Radius r (length units).
Total surface area and radius
Inputs: Total surface area S (square units); Radius r (length units).
Reading the notation
√ means a square root, ∛ means a cube root, and a superscript ² or ³ means a square or cube. Sine, cosine and tangent use angles converted from entered degrees. Where an inverse trigonometric function is used, its displayed angle is converted back to degrees. The ellipse perimeter is approximate; other formula labels describe the ideal mathematical model.
Use vertical height in the volume formula. Slant height must exceed the radius for a non-degenerate right cone.
Reference reading: Right circular cone at Wolfram MathWorld.