Cuboid Surface Area Calculator
SA = 2(lw + lh + wh) — two-way, plus volume, space diagonal, and unit conversion. 100% in your browser.
h = (SA/2 − l·w) / (l + w)
Worked Examples (recomputed)
1. Cuboid 10 cm × 8 cm × 6 cm → SA = 2(80 + 60 + 48) = 376 cm², volume = 480 cm³, diagonal = √200 ≈ 14.1421 cm.
2. Cuboid 2 m × 3 m × 4 m → SA = 2(6 + 8 + 12) = 52 m², volume = 24 m³, diagonal = √29 ≈ 5.3852 m.
3. (Reverse) SA = 94 m², l = 5 m, w = 4 m → h = (47 − 20) / 9 = 3 m. Check: 2(20 + 15 + 12) = 94 ✓
4. Cuboid 12 in × 18 in × 24 in → SA = 2(216 + 288 + 432) = 1,872 in² = 13 ft², volume = 5,184 in³, diagonal = √1044 ≈ 32.311 in.
Frequently Asked Questions (FAQ)
What is the cuboid surface area formula?
The surface area of a cuboid is SA = 2(lw + lh + wh), where l = length, w = width, h = height. Example: a 10 cm × 8 cm × 6 cm cuboid has SA = 2(80 + 60 + 48) = 376 cm².
How do I find the height of a cuboid from its surface area?
Use the reverse formula h = (SA/2 − lw) / (l + w). Example: SA = 94 m², l = 5 m, w = 4 m, so h = (47 − 20) / 9 = 3 m.
What is the cuboid volume formula?
The volume of a cuboid is V = l × w × h. Example: a 2 m × 3 m × 4 m cuboid has volume 24 m³.
How do I compute the space diagonal of a cuboid?
The space diagonal of a cuboid is d = √(l² + w² + h²). Example: a 2 m × 3 m × 4 m cuboid has diagonal √29 ≈ 5.3852 m.
What is the surface area of a cube with side 3.5 cm?
A cube is a special cuboid with l = w = h, so SA = 6s². For s = 3.5 cm: SA = 6 × 12.25 = 73.5 cm².
How do I convert cm² to m²?
Divide by 10,000 because 1 m = 100 cm, so 1 m² = 10,000 cm². Example: 2,200 cm² = 0.22 m².
Can this calculator be used with imperial units like inches and feet?
Yes. Enter dimensions in inches, feet, yards, or miles — surface area, volume, and diagonal results are automatically converted to all units. Example: a 12 in × 18 in × 24 in cuboid has area 1,872 in² = 13 ft².
When does the reverse formula have no solution?
If SA/2 − lw ≤ 0, the entered surface area is too small to cover the l × w base, so no positive height satisfies it. Increase SA or shrink l and w.
Keywords: cuboid surface area calculator, cuboid surface area formula, cuboid volume, cuboid space diagonal, rectangular prism surface area, how to find cuboid height from surface area, convert cm² to m², surface area of cuboid formula.
Free tool by NRTechStudio