HesapHanem

Wedge Volume Calculator

Enter the base length, width, top edge and height to find the wedge volume.

How it is calculated

The solid has a rectangular base of length a and width b. Its top is a single edge of length c parallel to side a, at height h above the base. The volume is V = (b × h ÷ 6) × (2a + c). The tool also reports the base area a × b and the combined factor 2a + c. All four measurements must be in the same length unit, and the result is in that unit cubed, the base area in that unit squared. The tool does not convert units, and its output labels the unit simply as "units". The base length a, width b and height h must be above zero; the top edge c may be zero but not negative. Setting c = 0 gives a pyramid-like tip and c = a gives a triangular prism.

Worked example

A wedge with base 10 long and 4 wide, top edge 6, and height 3. Factor: 2a + c = 2 × 10 + 6 = 26. Volume: (4 × 3 ÷ 6) × 26 = 2 × 26 = 52.000 units³. The base area is 10 × 4 = 40.000 units². Checks against the special cases: with c = 10 (equal to a) the volume is 60, which is the triangular prism (10 × 4 × 3 ÷ 2), and with c = 0 it is 40, which is one third of the box 10 × 4 × 3.

Try this example →

Common mistakes

  • Mixing units, for example length in metres and height in centimetres. The result is only meaningful if a, b, c and h share one unit.
  • Putting the edge c on the wrong side. The formula assumes the top edge is parallel to side a; if it runs parallel to b, swap the two measurements before entering them.
  • Entering the slanted side length as h. The height must be the perpendicular distance from the base to the top edge.
  • Entering the width of the top as c when it is a face. The top of a wedge is a line; if the top is a rectangle, the shape is a prism or frustum and needs a different formula.
  • Expecting the volume to be in litres or cubic feet automatically. It is expressed in whatever unit you entered, cubed, so convert afterwards.

About this calculator

A wedge is a solid with a rectangular base of length a and width b, tapering up to a single top edge of length c running parallel to one side, at height h — think of a doorstop or a section of roof ridge. Its volume is given by V = (b·h/6)(2a + c), a formula that reduces correctly to a pyramid's volume when c = 0 and to a triangular prism's volume when c = a.

This shape and formula show up in solid geometry coursework as a step beyond prisms and pyramids, and in practical form wherever a tapered wedge shape needs its volume calculated — earthworks and excavation estimating (a sloped cut or fill section), concrete wedge-shaped footings, roof ridge sections, and machine-shop parts milled to this profile all rely on the same formula.

Was this helpful?

You can pick up to 3 reactions.

Comments (1)

  • Editorial team

    Convert before you order material, because the result is in whatever unit cubed you measured in. Measure in feet and divide by 27 for cubic yards of gravel or concrete, or measure in centimetres and divide by 1,000,000 for cubic metres. Make sure the top edge c is the one running parallel to side a. What are you measuring, a ramp, a footing or a pile, and does the top edge run along the long side?

Popular calculators

Loan Calculator

Monthly payment, total interest and full amortization schedule.

Percentage Calculator

Percent change, percent of, and ratio calculations.

Discount Calculator

Calculate final price, savings, and discount amount.

BMI Calculator

Body mass index from height and weight (metric or imperial).

Age Calculator

Compute your exact age in years, months and days from a birth date.

Compound Interest Calculator

Calculate the final amount and interest earned with compounding.

All Calculators