A classic ridge tent is a triangular prism, a triangle stretched into a tunnel, and its volume is the triangle's area times the tunnel's length. Take a tent whose triangular end has a base of 10 feet and a height of 6 feet. The triangular area is one half times 10 times 6, which is 30 square feet. Stretch that triangle along a 12-foot length and the tent holds 30 times 12, which is 360 cubic feet of air, the number that decides whether two campers sleep comfortably or wake up elbowing each other. Toblerone bars, doorstop wedges, wedge-shaped concrete footings, attic spaces under pitched roofs, and optical glass prisms all share the same geometry: an extruded triangle, and one multiplication once the triangle's area is known.

What counts as a triangular prism, exactly

A triangular prism has two identical triangular faces, called the bases, joined by three rectangular faces. The two triangles are parallel and congruent, and the distance between them is the prism's length, sometimes also called its height, which is the first naming trap in this topic. The triangle itself has its own height, the perpendicular distance from its base to its opposite vertex, and the prism has a length, the distance between the two triangular ends. Keep those two heights in separate boxes in your head, because swapping them is the single most common triangular prism error. A right triangular prism has its rectangular faces perpendicular to the triangular ends, like a tent pitched squarely. An oblique triangular prism leans, like a wedge tipped to one side, but as long as the perpendicular distance between the ends is the same, the volume is the same, a fact mathematicians call Cavalieri's principle: sliding the layers sideways does not change how much space they fill.

The volume formula, and the two heights

The volume of a triangular prism equals the area of the triangular base times the prism's length. In symbols, with B for the triangular area and L for the length, volume equals B times L. The whole job is therefore finding B honestly, then multiplying once. If the triangle's base and height are known, B equals one half times base times height, so the full formula becomes volume equals one half times base times triangle height times length. The one half is not optional: forgetting it doubles every answer, and a doubled tent volume is the difference between a tent that fits two people and a tent that exists only on paper. Always check the units as you go: square feet times feet gives cubic feet, square inches times inches gives cubic inches, and a base area in square meters times a length in meters gives cubic meters. Mixing feet for the triangle and inches for the length silently corrupts the answer by a factor of 12 before any multiplication even starts.

Worked example: the ridge tent, step by step

Start with the tent from the opening paragraph and run every step in the open. The triangular end has a base of 10 feet and a perpendicular height of 6 feet, so its area is one half times 10 times 6, which is 30 square feet. The tent's length is 12 feet, so the volume is 30 times 12, which is 360 cubic feet. On this calculator, type 30 in the Variable A box and 12 in the Variable B box, and the Result box shows 360, the volume in cubic feet. Try the sanity check that catches most mistakes: a 30-square-foot triangle stretched 12 feet must hold more than 30 and less than a 30-foot cube, and 360 sits sensibly between those guardrails. If your answer comes out as 720, the one half was skipped. If it comes out as 60, the triangle height and the prism length were swapped somewhere along the way.

Worked example: a wedge doorstop and a concrete footing

Small numbers follow the same rule, which is worth proving because small jobs are where people stop checking. A wedge doorstop has a triangular face with a base of 4 inches and a height of 3 inches, so its area is one half times 4 times 3, which is 6 square inches. The wedge is 5 inches long, so its volume is 6 times 5, which is 30 cubic inches of rubber or wood. A wedge-shaped concrete footing has a triangular face with a base of 3 feet and a height of 2 feet, giving an area of one half times 3 times 2, which is 3 square feet, and a length of 8 feet, giving a volume of 3 times 8, which is 24 cubic feet of concrete. At roughly 0.6 cubic feet per 80-pound bag of premixed concrete, that footing takes 24 divided by 0.6, which is 40 bags before waste, and a sensible order adds 10 percent, about 44 bags. The doorstop and the footing differ by a factor of scale, not by a factor of method.

Finding the triangular area four ways

Not every triangle hands you a base and a height, so the base area has more than one route, and knowing all four saves most homework problems. For a right triangle, the two legs are already perpendicular, so the area is one half times one leg times the other: legs of 9 inches and 12 inches give one half times 9 times 12, which is 54 square inches, and a prism 10 inches long built on that triangle holds 54 times 10, which is 540 cubic inches. For a triangle with three known sides, Heron's formula finds the area: with sides of 13, 14, and 15 feet, the semi-perimeter is 21 feet, and the area is the square root of 21 times 8 times 7 times 6, the square root of 7,056, which is exactly 84 square feet, so a prism 6 feet long on that triangle holds 84 times 6, which is 504 cubic feet. For two sides and the angle between them, the area is one half times side times side times the sine of the included angle. For an equilateral triangle, the area is the square root of 3 divided by 4 times the side squared: a side of 8 inches gives about 27.71 square inches, and a prism 10 inches long on that triangle holds about 27.71 times 10, which is about 277.13 cubic inches.

Surface area is a different job

Volume needs only the triangular area and the length, but surface area needs the full triangle, and confusing the two jobs is a frequent source of wrong answers. The surface area of a triangular prism is twice the triangular area plus the perimeter of the triangle times the length: the two triangular ends plus the three rectangles wrapped around the sides. Take a prism on a 3-4-5 right triangle, 10 inches long. The triangular area is 6 square inches, the perimeter is 3 plus 4 plus 5, which is 12 inches, so the surface area is 2 times 6 plus 12 times 10, which is 12 plus 120, which is 132 square inches. This calculator performs the volume multiplication, base area times length, and does not ask for the triangle's sides, so surface area comes from the perimeter route worked by hand from the same measurements. If you only know the triangular area and the length, you can find the volume exactly but you cannot find the surface area, because the perimeter is not determined by the area alone.

Worked example: attic storage under a pitched roof

An attic is a triangular prism wearing a house, and its volume decides what actually fits up there. Suppose the gable triangle has a base of 24 feet, the width of the house, and a height of 9 feet, the rise from ceiling to ridge. Its area is one half times 24 times 9, which is 108 square feet. The house is 30 feet long, so the gross attic volume is 108 times 30, which is 3,240 cubic feet. That gross number is honest but not usable on its own: the low edges near the eaves are too short to stand in, and the access hatch, ductwork, and insulation eat real space, so a storage plan should count only the middle band where the headroom clears about 4 feet, not the full 3,240. The same caution applies to a tent: 360 cubic feet of air is not 360 cubic feet of sleeping space once sleeping bags, gear, and the sloping walls are counted. Volume is the starting measurement, not the final promise.

Running the formula backward

Often the volume is known and a dimension is missing, and the formula rearranges cleanly because it is a single multiplication. If a prism holds 600 cubic feet and its length is 20 feet, the triangular area must be 600 divided by 20, which is 30 square feet, and a triangle with a base of 10 feet then needs a height of 2 times 30 divided by 10, which is 6 feet, the tent numbers again, run in reverse. If a prism holds 540 cubic inches on a triangular area of 54 square inches, its length is 540 divided by 54, which is 10 inches. The backward check is also the fastest error detector: divide your volume by your length and see whether the triangular area that comes back matches the triangle you measured. If it does not, one of the three numbers is wrong, and the usual suspect is a triangle height entered as a prism length.

Scaling, units, and the oblique case

Scaling a prism teaches the difference between length and volume in one glance. Double only the length of the tent prism, from 12 feet to 24 feet, and the volume doubles, from 360 to 720 cubic feet. Double every dimension, base 20 feet, triangle height 12 feet, length 24 feet, and the area becomes 120 square feet and the volume becomes 120 times 24, which is 2,880 cubic feet, exactly 8 times the original, because volume scales with the cube of the scale factor. For unit conversions, the tent's 360 cubic feet converts to cubic yards by dividing by 27, giving about 13.33 cubic yards, to liters by multiplying by 28.3168, giving about 10,194.05 liters, and to US gallons by multiplying by 7.48052, giving about 2,692.99 gallons. The doorstop's 30 cubic inches converts to cubic feet by dividing by 1,728, giving about 0.0174 cubic feet, a reminder that small inch-scale volumes look tiny in feet and should stay in cubic inches. And for the oblique prism, remember Cavalieri's principle: a leaning wedge with the same triangular area and the same perpendicular distance between its ends holds exactly the same volume as the upright version, so measure the perpendicular distance, not the slanted edge, for the length.

How to use this calculator, honestly

This calculator performs the key multiplication at the heart of the triangular prism formula. Type the triangular base area in the Variable A box and the prism's length in the Variable B box, and the Result box shows the volume. For the tent, 30 and 12 give 360 cubic feet. For the doorstop, 6 and 5 give 30 cubic inches. For the right-triangle prism, 54 and 10 give 540 cubic inches. The tool does not compute the triangular area for you, so that area comes first, by the one-half-base-times-height route, the right-triangle leg route, Heron's formula, or the equilateral route, worked from your own measurements. Keep the area and the length in matching units, square feet with feet, square inches with inches, and check the backward division before ordering materials.

Five mistakes that cost real money

The first mistake is swapping the triangle's height with the prism's length, which answers a different prism than the one being built. The second is forgetting the one half in the triangular area, which doubles the volume and doubles the concrete order. The third is measuring the slanted edge of an oblique prism instead of the perpendicular distance between its ends, which overstates the length and the volume. The fourth is mixing units, square feet of area with an inch length, which corrupts the answer by a factor of 12. The fifth is quoting gross attic or tent volume as usable space, which promises headroom and storage that the sloping walls never deliver. Each of these is caught by the same two habits: name every measurement before entering it, and run the backward division as a check.

Related calculators on this site

If the triangular prism is part of a bigger job, three companion tools carry the next step. The triangle area calculator finds the triangular base area from base and height, three sides, or two sides and an angle, the exact input this page needs. The triangular pyramid calculator handles the tapering cousin, where the same base area and height give one third of the prism's volume. The volume of a cuboid calculator covers the rectangular box that a prism is often compared against, and the surface area of a cube page handles the box-shaped cousin when a wedge becomes a crate. Each one uses the same discipline: name the measurement before you enter it, keep units consistent, and check the answer by running the formula backward.

A classroom note on why extrusion works

Students sometimes ask why multiplying an area by a length gives a volume at all. The answer is a stack of slices: imagine the triangular end as a thin slice of paper, then stack identical slices along the length, one after another, until the prism is filled. Each slice contributes its area times its tiny thickness, and adding all the slices gives area times total length. That is why the prism rule works for any base shape, triangle, rectangle, or hexagon, and why the pyramid rule, where the slices shrink to a point, gives one third instead. The prism is the honest, constant cross-section case, and every other solid's volume formula is measured against it.

With the pre-filled defaults — Variable A 10, Variable B 5 — the Triangular Prism Calculator returns Result 50.0000. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.