Surface Area Calculator
Find the total surface area of common 3D solids by selecting a shape and entering its dimensions.
Example
A cylinder with radius r = 3 and height h = 7:
SA = 2πr(r + h)
= 2 × π × 3 × (3 + 7)
= 6π × 10
= 60π
≈ 188.4956 square units
How it works
Choose a solid, then enter the required dimensions (edge, length/width/height, radius, etc.). The total surface area updates live using the standard geometry formula for that shape.
Good to know
This Surface Area Calculator computes the total surface area of five common 3D solids — a cube, a rectangular box (prism), a sphere, a cylinder, and a cone — using the standard geometry formulas for each. You pick the shape, type in its dimensions, and the total area updates instantly, along with the formula it used and any helpful intermediate value (such as the cone's slant height). It's handy for students checking homework, teachers building examples, and anyone in DIY, packaging, or trades who needs to know how much material covers an object.
Reach for it when you need a "how much to cover" number rather than a "how much fits inside" number: paint or wrapping for a box, sheet metal for a cylinder, the fabric to skin a cone, or the glass to coat a sphere. Total surface area counts every outer face, so for a closed cylinder it includes both circular ends and the curved side; for a cone it includes the flat base plus the slanted side. If you only need part of that (say, a cylinder with no lid, or just the curved "lateral" area), this tool gives the closed-solid total, so subtract the faces you don't want.
Read the result as a plain area in square units of whatever unit you typed in — enter centimeters and you get cm², enter inches and you get in². The big number is the total; the smaller stats below show the shape, the formula applied, and an "extra" value like the computed slant length for a cone. Because surface area is two-dimensional, doubling an object's size multiplies its area by four, not two — useful to remember when scaling a design up or down.
A practical tip: keep every dimension in the same unit before you calculate, since the tool does not convert between units. For real-world material estimates, add a margin for overlaps, seams, waste, and offcuts — the geometric figure assumes a perfect, seamless skin with no allowance.
Frequently asked questions
How is the surface area of a cone calculated?
It uses SA = πr(r + l), where l is the slant height. The calculator finds l from the radius and vertical height using l = √(r² + h²), then adds the base circle (πr²) to the lateral surface (πrl).
What units does the result use?
The result is in square units of whatever unit you enter. If your dimensions are in centimeters, the surface area is in square centimeters (cm²); inches give square inches, and so on.
Is my data uploaded anywhere?
No — this calculator runs entirely in your browser; nothing is uploaded.
Is it free?
Yes, completely free with no sign-up and no limits.
People also ask
What is the difference between surface area and volume?
Surface area measures the total outer covering of a solid in square units, while volume measures the space inside it in cubic units. Surface area tells you how much material wraps the object; volume tells you how much it can hold.
What is the formula for the surface area of a cube?
A cube's total surface area is 6a², where a is the edge length, because a cube has six identical square faces. For example, a cube with 5 cm edges has a surface area of 6 × 5² = 150 cm².
How do you find the surface area of a sphere?
Use SA = 4πr², where r is the radius. A sphere has no flat faces, so this single formula covers its entire curved surface.
What is lateral surface area versus total surface area?
Lateral surface area is only the side (curved or slanted) surface, excluding the top and bottom faces. Total surface area adds those bases back in, so a closed cylinder's total includes both circular ends plus the curved side.
How do you calculate the surface area of a rectangular box?
Use 2(lw + lh + wh), where l, w, and h are the length, width, and height. This adds up the areas of all three pairs of matching faces.
Why does a cone's surface area need the slant height?
The cone's slanted side is measured along its sloping edge, not its vertical height, so the formula πr(r + l) uses the slant height l. The calculator derives it automatically from the radius and vertical height using l = √(r² + h²).
What units should I use for surface area?
Use any single unit of length consistently for every dimension, and the answer comes back in the matching square unit. Meters give m², feet give ft², and millimeters give mm²; the tool does not mix or convert units for you.
How much does surface area change when I scale an object up?
Surface area scales with the square of the size factor, so doubling every dimension multiplies the area by four and tripling it multiplies the area by nine. This is why larger objects need disproportionately more covering material.
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