Pyramid Volume Calculator
Volume of a rectangular pyramid from its base and height, in cubic feet and cubic yards, with the box of the same base and height shown for comparison.
With base length 6 ft, base width 6 ft, height, straight up from the base 9 ft, pyramid volume comes to 108.00 cu ft — volume. It is reached in 5 steps, the last of which is base_area * height / 3, and each one is printed on the page with its numbers filled in. The formula is the one published by Wolfram MathWorld, not an approximation fitted to it.
Formula and sources checked · How we check
Base length 6 ft, Base width 6 ft, Height, straight up from the base 9 ft
108.00 cu ft
Volume for the example below. Editing a field recomputes the calculator below; this figure holds the answer the page was loaded with.
It is written into the HTML rather than drawn by a script, so a search engine reading this page without running JavaScript still finds an answer.
- Base area
length * width36 sq ft- Volume
base_area * height / 3108 cu ft- A box of the same base and height
base_area * height324 cu ft- Volume in cubic yards
volume / 274 cu yd- Slant height up the middle of a face
sqrt(pow(height, 2) + pow(width / 2, 2))9.487 ft
Worked example
A 6 × 6 base rising 9 ft holds 108 cu ft, or 4 cu yd. A box on the same base and height holds 324 cu ft — exactly three times as much, the same one-third that governs a cone.
How to work it out yourself
- 1.Measure the base along both sides and multiply for the base area.
- 2.Measure the height straight up from the centre of the base, not along a sloping face.
- 3.Multiply the base area by the height and divide by three.
- 4.Divide by 27 for cubic yards if you are ordering material.
The formula
- Base area
length * width - Volume
base_area * height / 3 - A box of the same base and height
base_area * height - Volume in cubic yards
volume / 27 - Slant height up the middle of a face
sqrt(pow(height, 2) + pow(width / 2, 2))
Source: Wolfram MathWorld — pyramid, NIST Digital Library of Mathematical Functions
Questions people actually ask
- Which height do I measure?
- The perpendicular one — straight up from the base to the apex. Measuring up a sloping face gives the slant height, which is longer and produces a volume that is too large.
- Why one third again?
- Any solid that tapers evenly to a point holds a third of the prism on the same base. It is the same fact as the cone, stated for a rectangular base rather than a round one.
Related
- Cone Volume CalculatorVolume of a cone from its diameter and height, in cubic feet, cubic inches and gallons, with the radius and the base area shown separately.
- Cubic Yard CalculatorCubic yards for any footprint and depth, with a waste allowance and the weight of the debris if you are hauling it away.
- Square Footage CalculatorSquare footage of a room, wall, border, gable end, ring or triangle from feet-and-inches measurements, with a waste factor and the cost.
- Diagonal & Rafter Length CalculatorHypotenuse of a right triangle in feet and inches — brace lengths, rafter runs, and squaring a layout.
- Circle CalculatorArea, circumference and radius of a circle from its diameter — in square feet and square inches.
- Tank & Cylinder Volume CalculatorVolume of a cylinder in cubic feet, US gallons and litres — round tanks, pools, culverts and post holes.
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