NumberTally Surface Area Calculator
Find the total surface area of a rectangular box, cylinder, or sphere. Pick the solid, enter the dimensions, and get the answer with the formula and step-by-step working — plus the volume and the surface-to-volume ratio. Free, no sign-up.
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The three surface-area formulas
Box: 2(lw + lh + wh) — add the three distinct face pairs and double. Cylinder: 2πr² + 2πrh — the two circular caps plus the unrolled side (a rectangle h tall and 2πr long). Sphere: 4πr² — exactly four times the area of its great circle.
Surface area vs volume
Surface area is what you paint; volume is what you fill. The SA÷V ratio matters in the real world: small objects have huge ratios (why crushed ice cools drinks faster), and it's why large animals overheat more easily than small ones.
Frequently Asked Questions
How do you find the surface area of a cube?
A cube is a box with all sides s: SA = 6s² — six identical square faces. A 3-unit cube has surface area 54.
How do you find the surface area of a cylinder?
SA = 2πr² + 2πrh: the two circular ends plus the lateral (side) area. The side unrolls into a rectangle of width 2πr and height h.
How do you find the surface area of a sphere?
SA = 4πr². A sphere of radius 3 has surface area 36π ≈ 113.10 — exactly four times the area of a circle with the same radius.
What is the difference between surface area and volume?
Surface area (square units) measures the outside skin; volume (cubic units) measures the inside capacity. A hollow ball's paint need is surface area; its air capacity is volume.
Do I include the bottom of an open container?
For an open-top box or cylinder, subtract one base: box SA becomes 2lh + 2wh + lw, cylinder becomes πr² + 2πrh. This calculator gives the closed-solid total.