📐 Wedge Volume Calculator
Calculate volume and dimensions of wedge-shaped objects
Enter Wedge Dimensions
a=base, c=top, b=width,
h=height
📊 Wedge Results
Base Width (b)
8 cm
Base Length (a)
12 cm
Top Length (c)
6 cm
Height (h)
5 cm
Volume
360 cm³
Surface Area
334.7 cm²
Slant Length
7.81 cm
Slope Angle
39.8°
📝 Step-by-Step Solution
Given: b = 8 cm, a = 12 cm, c = 6 cm, h = 5 cm
Wedge volume formula: V = (b × h / 6) × (2a + c)
V = (8 × 5 / 6) × (2 × 12 + 6) = (40 / 6) × 30
V = 6.667 × 30 = 200 cm³
Alternative: V = b × h × (a + c) / 2 = 8 × 5 × 9 = 360 cm³ (trapezoid
cross-section)
📐 Wedge Formulas
Volume: V = (b × h / 6) × (2a + c) [standard wedge]
Alternative: V = (b × h × (a + c)) / 2 [trapezoid method]
If c = 0 (triangular prism): V = (b × h × a) / 2
If c = a (rectangular prism): V = b × h × a
Slant: s = √(h² + ((a-c)/2)²)
Understanding Wedges
📐 What is a Wedge?
A 3D shape with rectangular base and a sloped top that tapers to a shorter edge. Like a doorstop or ramp.
📏 Key Dimensions
b = width, a = base length, c = top length, h = height. When c = 0, it's a triangular prism (right angle wedge).
🔺 Cross-Section
Perpendicular slice is a trapezoid (or triangle if c=0). The formula averages the two parallel lengths.
🛠️ Applications
Ramps, doorstops, chocks, keys. Wedges convert a small input force into a large splitting force.
Frequently Asked Questions
What is the volume formula for a wedge?
V = (b × h / 6) × (2a + c). Or equivalently V = (b × h × (a + c))
/ 2 using trapezoid cross-section method.
What are the dimensions of a wedge?
b = base width, a = base length, c = top length, h = height. The
top edge c is parallel to base length a but shorter.
What if top length is zero?
Becomes a triangular prism. When c = 0, V = (b × h × a) / 2. Like
a right-angle wedge or ramp.
What if top equals base length?
Becomes a rectangular box. When c = a, V = b × h × a. No
slope—it's a prism.
How do I find surface area?
Sum of all 5 faces. Base rectangle + 2 side triangles + 1 back
rectangle + 1 sloped face.
What is the slant length?
s = √(h² + ((a-c)/2)²). The distance along the sloped surface from
bottom edge to top edge.
How do I find slope angle?
θ = arctan(h / ((a-c)/2)). The angle of the sloped face relative
to horizontal.
Is a doorstop a wedge?
Yes, classic wedge shape. Rectangular base tapering to a thin edge
(c ≈ 0). Used to convert horizontal force to vertical.
What is the difference from prism?
Prism has uniform cross-section. Wedge tapers—one end narrower
than the other. Prism: c = a. Wedge: c < a.
How do I find height from volume?
h = 6V / (b(2a + c)). Rearrange the volume formula. Our calculator
solves this automatically.
Real-world wedge examples?
Ramps, chocks, axes, chisels, plows. Also architectural features,
bridge supports, and machine components.
Can the top be longer than base?
Formula still works mathematically. If c > a, you have an inverted
wedge (wider at top). Simply swap a and c in interpretation.
How accurate for irregular wedges?
Exact for true geometric wedges. Real objects may have rounded
edges or curved surfaces affecting actual volume.
What is mechanical advantage of wedge?
MA = length / width approximately. Longer, thinner wedges have
greater mechanical advantage for splitting.
How do I convert units?
All dimensions same unit. Our calculator handles unit conversion
for volume output (cm³, L, gallons, etc.).
Is a pyramid a wedge?
No, different shapes. Pyramid has pointed apex, wedge has an edge.
Pyramid tapers to a point; wedge tapers to a line.
What is wedge cross-section?
Trapezoid (or triangle if c=0). Perpendicular slice through width
direction shows the tapered shape.