DIY Cost Tools
Square Pyramid Calculator
MATH & GEOMETRY CALCULATOR
Calculate volume, slant height, and surface areas of a right square pyramid.
Use the same length unit throughout. All fields are required. Area formulas do not apply to an oblique pyramid. Height must be perpendicular to the base.
How to use this calculator
Enter your dimensions and select Calculate. Length results use your input unit, areas use its square, and volumes use its cube. Retain measurement precision until the final answer.
Formula and explanation
V = s²h/3; slant height = √(h²+(s/2)²); lateral area = 2s × slant height; total area = s² + lateral area
The apex must sit directly above the center of the square base.
Worked example
For Base edge (units) = 6, Perpendicular height (units) = 4, results are Volume (cubic units): 48; Face slant height (units): 5; Lateral area (square units): 60; Total area (square units): 96.
Important limitations
Area formulas do not apply to an oblique pyramid. Height must be perpendicular to the base.
Ideal geometry does not account for manufacturing tolerances or measurement uncertainty. This is a calculation aid, not a structural design or building-code approval. Absolute inputs must not exceed one trillion.
Frequently asked questions
Is slant height an edge?
No; it runs from an edge midpoint to the apex across a face.
Is the base included?
Only in total surface area.
Can I mix inches and centimeters?
Convert all lengths to one unit first. Mixed units produce incorrect results.
Why did my result disappear?
Blank, invalid, or out-of-range inputs clear the previous result and display an instruction.
Review notes
Reviewed October 1, 2026. Default results were checked against the displayed formulas. Script tests covered blank, negative, nonfinite, and excessive inputs. Results run locally in your browser.