Surface Area Calculator
Calculate surface area and lateral area for cubes, rectangular boxes, cylinders, spheres, and cones. Includes paint coverage and material cost estimates.
Total Surface Area
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Lateral Surface Area —
Extended More scenarios, charts & detailed breakdown ▾
Total Surface Area
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Lateral SA —
Professional Full parameters & maximum detail ▾
Surface Area
Total Surface Area (units²) —
Total Surface Area (sq ft) —
Material Estimates
Paint Needed (gallons) —
Material Cost —
How to Use This Calculator
- Select the Shape (cube, box, cylinder, sphere, or cone).
- Enter the required dimensions (side, radius, height).
- Total and lateral surface areas are computed instantly.
- Use the dedicated Box, Cylinder, or Sphere tabs for detailed results.
- The Professional tab estimates paint gallons and material cost.
Formula
Cube: 6s² | Box: 2(lw+lh+wh) | Cylinder: 2πr(r+h) | Sphere: 4πr² | Cone: πr(r+l)
Example
Sphere r=7: SA = 4π×49 ≈ 615.75 units². Box 5×4×3: SA = 2(20+15+12) = 94 units².
Frequently Asked Questions
- Surface area is the total area covering the exterior of a 3D solid, measured in square units (cm², m², ft²). For flat-faced solids like cubes and boxes, it is the sum of the areas of all faces. For curved solids like spheres, cylinders, and cones, it involves curved surface formulas. Surface area determines how much material is needed to wrap or coat an object, how quickly it transfers heat, and how much paint is needed to cover it. Unlike volume (which is 3D), surface area is always a 2D measurement.
- A cylinder has two circular caps and one curved side. Total SA = 2πr² + 2πrh = 2πr(r + h), where r is the radius and h is the height. The lateral SA (just the curved side, without caps) = 2πrh. For r = 5, h = 10: Total SA = 2π × 5 × (5 + 10) = 2π × 5 × 15 ≈ 471.24 square units. Lateral SA = 2π × 5 × 10 ≈ 314.16. The lateral surface unrolled is a rectangle with width 2πr (circumference) and height h.
- Total surface area (TSA) includes every face: all sides plus all bases. Lateral surface area (LSA) includes only the side surfaces, excluding the top and bottom bases. For a cylinder: LSA = 2πrh (curved side only), TSA = 2πrh + 2πr² (sides plus both caps). For a cone: LSA = πrl (slant surface), TSA = πrl + πr² (adds the circular base). Lateral SA is used when calculating paint for tank walls, labels on cans, or the skin of a prism.
- A cone has one circular base and one curved slant surface. Total SA = πrl + πr², where r is the base radius and l = √(r² + h²) is the slant height. The lateral (slant) surface area is πrl. For r = 4, h = 3: l = 5, Lateral SA = π × 4 × 5 ≈ 62.83, Total SA = π × 4 × (5 + 4) ≈ 113.10 sq units. The lateral surface can be unrolled into a flat circular sector with radius l and arc length 2πr.
- Divide the surface area in square feet by the paint coverage rate in square feet per gallon. Standard interior paint covers approximately 350–400 sq ft per gallon; exterior paint covers about 300–350 sq ft per gallon. For example, to paint a room with 800 sq ft of wall: 800 ÷ 350 ≈ 2.29 gallons, so purchase 3 gallons to be safe. Always account for two coats: multiply by 2. The Professional tab of this calculator automates this, letting you input the coverage rate and number of coats.