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Volume of a Triangular Prism Calculator

Range: 0 cm² – 1,000,000,000,000,000,000 cm²

Range: 0 cm – 1,000,000,000 cm

Result

60.0000 cm³

Volume

A volume of a triangular prism calculator takes the area of the triangular end and the prism's length, and returns how much the prism holds, in cubic centimetres. It is one multiplication. That is the whole page, and the brevity is deliberate rather than lazy: once you have the area of the cross-section, the volume of any prism is that area times how far the prism runs, and no amount of extra input changes the arithmetic. The reason to have a page for it anyway is that the area is often the number you already have. A drawing will quote a triangular section as so many square centimetres, a previous calculation will have produced it, a supplier's sheet will list it — and asking you to break that area back down into three side lengths, only for the page to multiply them together again, would be busywork. What the page is not, is a substitute for the umbrella version. If what you have is the three sides of the triangle rather than its area, this page has no box to put them in, and the honest answer is to go to the triangular prism page, or to work the area out first on the triangle area or Heron's formula page and then come back. The one thing worth knowing about the multiplication is how forgiving it is: with a base area of 6 and a length of 10 the answer is exactly 60, and the same base area with a length of 1 gives exactly 6, because there is no division and no square root anywhere in the path.

The volume of a triangular prism from its base area and length

Base area (cm²)Length (cm)Volume (cm³)
61060
616
11010
0100
600
2.5410
32.57.5
1.51.52.25

Eight prisms and three columns, because the page has one multiplication and one answer. The first row is the reconciliation row and the one to remember: a base area of 6 with a length of 10 gives 60, and 6 is exactly the area of a 3-4-5 triangular end, so the umbrella page prints the same 60 for those sides with the same length. The second row is the self-check — with a length of 1 the volume equals the base area, which confirms the multiplication is doing nothing else. The third row is the mirror of it, where a base area of 1 makes the volume equal the length. The fourth and fifth rows are the two ways to get a volume of zero, which are not the same situation: an area of zero is an end that has been flattened into a line, and a length of zero is a prism with no depth. The last two rows carry decimals — a fractional length in the seventh, both inputs fractional in the eighth — and the multiplication is still exact there because nothing is ever divided. Every value here is recomputed from its two inputs when the page is built, in centimetres, and the four decimals are the same four decimals the results panel uses.

Formula

V = A(base) × L

Base area
The area of the triangular end, in square centimetres. This is the cross-section — the shape you would see if you sliced the prism across, at right angles to its length
Length
How far the prism runs, in centimetres — the distance between the two identical triangular ends, measured along the direction of travel
Volume
How much the prism holds, in cubic centimetres. The base area multiplied by the length, and nothing else
A(base) × L
One multiplication. There is no division and no square root anywhere in this page, so for inputs that are exactly representable the answer is exact rather than rounded
Any prism
This is the rule for every prism, not just the triangular ones. A cuboid is a rectangular cross-section times a length, a cylinder is a circle times a length, and this page is a triangle times a length
Four decimal places
How wide the reading is written. Two whole numbers always give a whole number, so the decimals only come into play when the area or the length has a fraction in it
Cubic centimetres
The unit of the answer whatever the dropdowns say. This is a volume, so the conversion is cubed — a prism measured in inches comes back as cubic centimetres, and you divide by 16.387 to read it in cubic inches

The page is for anyone who is holding an area rather than three sides. Concrete and earthworks are the largest group: a triangular kerb, a berm, a trench with a triangular section, all specified in a drawing that gives the cross-section as an area and asks how much concrete the run needs. Because those are ordered by the cubic metre and billed on delivery, the number has to be right before the truck arrives, and the drawing's area is the authoritative figure rather than something to be recomputed from sides. Wrap and coating jobs use the same page when they are working from a quoted section area. Then there is the small group of jobs where the end is not a triangle at all in any convenient sense — a curved or irregular section whose area has been measured or estimated rather than calculated. That is the one place this page does something the umbrella page cannot: any cross-section with a known area works here, because the multiplication never asks what shape the area came from. The triangular framing on the page is there because that is how people search, not because the arithmetic cares.

Worked examples

  1. A base area of 6 and a length of 10

    1. Multiply the base area by the length: 6 × 10 = 60

    The pair the page loads with, and the reconciliation row: an area of 6 is exactly what a 3-4-5 triangular end has, so the umbrella page prints the same 60 for a 3-4-5 end with a length of 10. Enter the same two numbers on either page and you get the same volume — one of them worked the area out from the sides and the other was handed it.

  2. A base area of 6 and a length of 1

    1. Multiply the base area by the length: 6 × 1 = 6

    The self-checking row. With a length of one, the volume is numerically the same as the base area, which is the quickest way to confirm that the multiplication is doing what you think it is and that nothing has been slipped in on the way.

  3. A base area of 2.5 and a length of 4

    1. Multiply the base area by the length: 2.5 × 4 = 10

    An area with a fraction in it, which is what a halved triangle area or a measured section often gives. The multiplication is exact and there is no division to follow it, so the answer is a clean 10 rather than a rounded approximation of one.

  4. A base area of 6 and a length of 0

    1. Multiply the base area by the length: 6 × 0 = 0

    A length of zero means the prism has no depth at all and holds nothing. Zero is a real input rather than a blank box, so this is a real answer — and it is a genuinely different situation from the degenerate end you would get by making the base area zero, even though both print a volume of zero.

Limitations

This page takes a base area and a length and nothing else. It cannot work from the three sides of the triangle — that is the triangular prism page's job, or the triangle area and Heron's formula pages if you want to arrive at the area yourself and come back. It gives no surface area and no lateral area, which the umbrella page does give, so if you need to know how much wrap goes around the prism this is the wrong page. It assumes the prism is right: the two ends parallel and identical, with the sides running perpendicular to them. The answer is always in cubic centimetres whatever the dropdowns say, and since this is a volume the conversion is cubed — a section measured in inches comes back as cubic centimetres, and you divide by 16.387 rather than by 2.54. Four decimal places is a display width rather than a claim about precision. Zero is accepted for either input and gives a volume of zero, which is a real answer rather than a missing one. Nothing here handles a hollow prism, wall thickness, a tapering or oblique shape, or an allowance for waste when the material is ordered.

Frequently asked questions

Where do I get the base area from?
If you measured the three sides of the triangular end, use Heron's formula on its own page, or the triangular prism page which does it for you and returns the volume directly. If the area is already on a drawing or a supplier's sheet, type it straight in — that is exactly the case this page is for, and the multiplication never asks where the number came from.
Why is there a separate page for this?
Because the input is different, and so is the person using it. The triangular prism page starts from three side lengths and returns three readings; this one starts from an area you already have and returns one. Somebody holding a drawing that quotes a section area has no use for a page asking for three sides, and somebody holding three sides has nothing to type here.
Is the base the bottom face?
Not necessarily, and it is worth being clear about. Here 'base' means the cross-section — the triangular end you would see if you sliced the prism across at right angles to its length. A prism lying on one of its rectangular faces has a triangle standing up, and the bottom face is a rectangle; the area this page wants is still the triangle's.
Does the rule work for other shapes?
Yes — the volume of any prism is its cross-section's area times its length, whatever shape that cross-section is. A cuboid is a rectangle times a length, a cylinder is a circle times a length. The multiplication never inspects the shape, which is also why this page works for a section whose area was measured rather than calculated.
Do the units matter?
The dropdowns change what you type in, not what comes out. The reading is always in cubic centimetres, and because this is a volume the conversion is cubed: divide by 16.387 to read a cubic-centimetre answer in cubic inches, not by 2.54. Entering a section in square inches and reading the volume as cubic inches is the error to watch for.
What if the length is zero?
The volume is zero, and that is correct: a prism with no length has its two ends brought together and holds nothing. Zero is treated as a real value rather than as an empty box, so the page prints a result. Leaving a box blank is different — there is nothing to multiply and the page shows no result at all.

References

Related calculators

Triangular Prism CalculatorVolume and surface area of a prism with triangular ends.Triangle Area CalculatorHalf a base times the perpendicular height above it.Heron's Formula CalculatorTriangle area from three side lengths, by Heron's formula.Cuboid Volume CalculatorVolume and surface area of a rectangular box.