Example 1
- Base area: 36
- Height: 9
108.00
Square 6 by 6 (area 36) and h = 9: 108. One third of prism 324.
Pyramid volume calculator
Compute the base area first, then type it with the height from the tip down to that base plane. The calculator takes one third of the product. A 6 by 6 square has area 36; at h = 9 you get 108.00, one third of prism 324.
V = ⅓ base area h. A prism is on the prism volume calculator. A cone is on the cone volume calculator.
Result
Base area (cm²) and Height h (cm). Volume shows up here.
How it works
A pyramid has one third the volume of a prism with the same base area and the same height. V = ⅓ base area × h multiplies a ready area by h and divides by three. Base area is area, for example 6×6 = 36 for a square, not the edge 6. Typing 6 instead of 36 understates the result sixfold.
The first card example, area 36 and h = 9, is 108.00. That prism would be 324. The pair 100 and 3 also yields 100.00, because ⅓×100×3 = 100: a large base, a small height. Area 24 and h = 6 is 48.00, the same as area 12 and h = 12. A 4 by 4 square (area 16) at h = 12 comes out 64.00.
Compute base area on the rectangle, triangle, or circle page, type it as base area, then height from the apex to the base plane. Click Calculate. Height drops perpendicular. An edge on a lateral face is longer and is not h. A comma and a period are the same.
A cone does the same with a circle: πr² stands in for base area. A ready circle belongs on the cone volume page; here you can type πr² yourself if you want. A cube of edge 6 has volume 216; a pyramid on a 36 square with h = 6 would be 72, not 216.
The base can be a square, a triangle, a rectangle, or any polygon, as long as you type area, not perimeter. Switching to inches relabels the result as in³. If area is in cm² and h is in cm, the result is in cm³. Mixing cm² with inches breaks the scale.
The pair area 9 and h = 9 gives 27.00, the same digits as a cube of edge 3, a different solid. The formula does not need the two numbers to look alike. What matters is that the first number is area and the second is perpendicular height.
How to use
- Compute base area on the rectangle, triangle, or circle page. A 6 by 6 square is 36, not 6.
- Type that area as base area, in cm² or in² matching the label.
- Type height from the apex to the base plane, straight down, in cm or inches.
- Click Calculate. At 36 and 9 you get 108.00, one third of prism 324.
- Open a cone with a circular base on its own page, unless you type base area = πr² yourself.
Formula
V = (1/3) × base area × h
Base area is area, not an edge. Typing 6 instead of 36 understates a 6 by 6 square sixfold.
One third of base area at a 6 by 6 square
One third of area times height. A 6 by 6 square has area 36; at h = 9 you get 108.00, one third of 324.
- V
- Volume (1/3) × base area × h. 36 and 9 give 108.00. 24 and 6 give 48.00. A prism would keep 324.
- h
- Height from the tip to the base plane. 9 with area 36 is 108.00. A short 3 with area 100 is also 100.00.
- cm³
- Volume unit on the metric label. 36 and 9 print 108.00 cm³. Type 36, not edge 6.
Examples
Example 2
- Base area: 24
- Height: 6
48.00
Area 24, h = 6, 48.00.
Example 3
- Base area: 100
- Height: 3
100.00
Large base 100, short h = 3, also 100.00.
Example 4
- Base area: 12
- Height: 12
48.00
Area 12, h = 12, 48.00, a different pair from 24 and 6.
Example 5
- Base area: 50
- Height: 6
100.00
Area 50, h = 6, 100.00.
Example 6
- Base area: 9
- Height: 9
27.00
Area 9, h = 9, 27.00. Same digits as a cube of edge 3, different solid.
Example 7
- Base area: 48
- Height: 5
80.00
Area 48, h = 5, 80.00.
Example 8
- Base area: 16
- Height: 12
64.00
Square 4 by 4 (area 16) and h = 12: 64.
Frequently asked questions
What do area 36 and h = 9 give?
108.00. A prism with those numbers would be 324. One third, the same area and the same h.
Do I type a base edge or the area?
The area. A square of side 6 has area 36, not 6. Typing 6 instead of 36 understates volume sixfold.
How is a pyramid different from a prism?
A pyramid has one third the volume at the same base area and h. At 36 and 9 it is 108 versus 324.
Do I compute a cone here?
Only if you type base area = πr² yourself. A ready circle belongs on the cone volume page.
Is height a lateral edge?
h drops perpendicular onto the base. An edge on a face is longer and is not an input.
Must the base be a square?
No. Triangle, rectangle, polygon. What matters is that you type area, not perimeter.
Is a cube of edge 6 this pyramid?
A cube 6³ = 216. A pyramid on area 36 with h = 6 is 72. Different solid.
Why do 100 and 3 give 100.00?
Because ⅓×100×3 = 100. Large base, small height. The formula does not need similar numbers.
What units is the result in?
If area is cm² and h is cm, the result is cm³. Mixing cm² with inches breaks the scale.
Where do I get area for a 6 by 6 square?
On the rectangle area page. 6 times 6 is 36, then return here with height.
Knowledge sources
The calculator computes the same formula as the definition below.
Page updated in 2026.