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.
Base edge and vertical height
Inputs: Base edge a (length units); Vertical height h (length units).
Base edge and face slant height
Inputs: Base edge a (length units); Face slant height l (length units).
Volume and base edge
Inputs: Volume V (cubic units); Base edge a (length units).
Total surface area and base edge
Inputs: Total surface area S (square units); Base edge a (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.
Do not substitute a lateral edge for a face slant height. The apex must lie over the base centre for these calculators.
Reference reading: Right square pyramid at Wolfram MathWorld.