Pyramid Volume Calculator
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 36 * 9 / 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.
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.
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
6 * 636 sq ft- Volume
36 * 9 / 3108 cu ft- A box of the same base and height
36 * 9324 cu ft- Volume in cubic yards
108 / 274 cu yd- Slant height up the middle of a face
sqrt(pow(9, 2) + pow(6 / 2, 2))9.487 ft
Several at once
A job is rarely one of anything. Work out the first, add it, change the figures and add the next — the list keeps what each line was, and totals them.
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
6 * 6 - Volume
36 * 9 / 3 - A box of the same base and height
36 * 9 - Volume in cubic yards
108 / 27 - Slant height up the middle of a face
sqrt(pow(9, 2) + pow(6 / 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 liters — round tanks, pools, culverts and post holes.
Put this calculator on your site
Free, no attribution required beyond the link.
<iframe src="https://rulecalculators.com/embed/pyramid-volume" width="100%" height="420" style="border:1px solid #e7e4de;border-radius:12px" title="Pyramid Volume Calculator"></iframe>