Wedge volume calculator
Wedge volume from V = (b·h/6)·(2a + c) with base a × b, top edge c and height h — c = 0 collapses to a pyramid and c = a to a triangular prism — cross-checked against the prismatoid formula h/6·(A₁ + 4Aₘ + A₂).
Runs in your browserEvery computation happens in your browser — your data never leaves this device.
Volume result
V = (b·h/6)·(2a + c), cross-checked with the prismatoid formula.
Enter the dimensions to calculate the wedge volume
Volume: 0 · Base area: 0 · Mid section: 0
What this tool does
- Earthwork: volume of a wedge-shaped stockpile such as gravel banked against a wall.
- Building components: the wedge of concrete under a stair stringer or the space under a pitched roof.
- Machine design: material and weight of wedges and tapered shims.
Example
Input
4
Output
楔形体体积：50（长度单位 u，体积单位 u³） 尺寸：底面 4 × 5，顶棱 2，高 6 公式 V = (b·h/6)·(2a + c) = (5 × 6 / 6) × (2 × 4 + 2) = 50 拟柱体公式校验 h/6·(A₁ + 4Aₘ + A₂) = 50（两者应完全一致） 底面积 A₁ = ab：20；中截面 Aₘ = b(a + c)/4：7.5；顶棱面积为 0 形状判定：一般楔形体
With a=2, b=3, c=1 and h=4 the volume is (3×4/6)×(2×2+1) = 10, matching the prismatoid formula exactly.
Frequently asked questions
Where does the formula come from?
V = (b·h/6)(2a + c) is the engineering handbook form for a wedge, and it also follows from the prismatoid formula V = h/6·(A₁ + 4Aₘ + A₂) with A₁ = ab, A₂ = 0 and Aₘ = b(a + c)/4. The tool computes both and compares them.
What range does c take?
0 ≤ c ≤ a. At c = a the top face is as long as the base and the solid becomes a triangular prism (half a box) with volume abh/2; at c = 0 it collapses to a pyramid with volume abh/3. Values above a are rejected.
How is a wedge different from a frustum?
A frustum has similar top and bottom polygons (the top is a scaled copy of the base), while a wedge tapers to a single edge or a shorter rectangle. Frusta use V = h/3·(A₁ + √(A₁A₂) + A₂); wedges use the formulas here.
Any unit restrictions?
None — just keep all four dimensions in the same unit: metres give cubic metres, centimetres give cubic centimetres. The tool does not convert.
What is the prismatoid check?
It is the same solid computed a second way: h/6·(A₁ + 4Aₘ + A₂). Both formulas agree exactly, so the line confirms the parameters were entered correctly.
Keywords：楔形体积wedge volume楔形体拟柱体公式四棱锥三棱柱土方计算体积公式