Prism Volume Calculator Formula
Understand the math behind the prism volume calculator. Each variable explained with a worked example.
Formulas Used
Volume
volume = l * w * hSurface Area
surface_area = 2 * (l * w + l * h + w * h)Diagonal
diagonal = sqrt(pow(l, 2) + pow(w, 2) + pow(h, 2))Variables
| Variable | Description | Default |
|---|---|---|
l | Length | 10 |
w | Width | 5 |
h | Height | 3 |
How It Works
Rectangular Prism (Box) Formulas
Volume
V = l × w × h
Surface Area
SA = 2(lw + lh + wh)
Space Diagonal
d = sqrt(l² + w² + h²)
The space diagonal runs from one corner to the opposite corner through the interior of the box.
Worked Example
Box with length 10, width 5, height 3.
l = 10w = 5h = 3
- 01Volume = 10 × 5 × 3 = 150
- 02Surface area = 2(50 + 30 + 15) = 2 × 95 = 190
- 03Diagonal = √(100+25+9) = √134 ≈ 11.5758
Frequently Asked Questions
What is a prism?
A prism is a 3D shape with two parallel, identical bases connected by rectangular faces. A rectangular prism (box) is the most common type.
Is a cube a prism?
Yes, a cube is a special rectangular prism where all three dimensions are equal.
What is the space diagonal?
The space diagonal is the longest line segment inside the box, connecting opposite corners through the interior. It uses a 3D version of the Pythagorean theorem.
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Open Prism Volume Calculator