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
Ready to run the numbers?
Open Prism Volume Calculator