What the Surface Area Calculator does
This calculator gives the total surface area, the lateral (side or curved) surface area and the volume of nine common solids - cube, cuboid, cylinder, sphere, hemisphere, cone, square prism, triangular prism and square pyramid. Pick the shape, type its measurements in any length unit, and every answer appears with its formula and your numbers substituted into it, so you can follow or copy the working.
Surface area is the total area of every face or curved surface that encloses a solid: what you would need to paint it, wrap it or make it from sheet material. Volume is the space inside. The two grow differently - double every length of a box and its surface area goes up four times while its volume goes up eight times - which is why both are shown together. Everything runs in your browser and the full value of pi is used, with rounding only at the end.
How to use it
- Choose the shape from the list and the unit your measurements are in - millimetres, centimetres, metres, inches, feet or yards. All lengths must use the same unit.
- Enter the measurements. A cylinder, sphere, hemisphere and cone need the radius, which is half the diameter. For a cone or a square pyramid you can give either the vertical height or the slant height; switch with the buttons above the fields.
- For a triangular prism enter the three sides of the triangle at the end and the length of the prism. The triangle's area is worked out with Heron's formula, so it does not need to be right-angled.
- Read the total surface area at the top, then the lateral or curved area, the volume in cubic units and the capacity in litres. The working list shows each formula with your numbers, ready to copy into homework or a quote.
Reading the results
Total surface area (TSA) counts every surface, including the top and bottom. Lateral surface area leaves out the bases: for a cylinder it is the label round a tin, for a prism the rectangular sides, for a pyramid the four triangles. When the side is curved - cylinder, cone, sphere, hemisphere - the same idea is called the curved surface area (CSA).
Area units are squared and volume units are cubed. If you measured in centimetres, the area is in square centimetres (cm²) and the volume in cubic centimetres (cm³); 1,000 cm³ is exactly one litre, which is the capacity figure shown.
A hemisphere here is a solid half-ball with its flat circular face, so its total area is 3πr². A hollow bowl has only the curved 2πr², which is shown as the curved surface area.
Worked example: the label and the metal of a tin can
A food tin is about 7.6 cm across and 11 cm tall, so its radius is 3.8 cm. The label wraps the curved side only: CSA = 2πrh = 2 × π × 3.8 × 11 = 83.6π ≈ 262.64 cm².
The whole tin, including both ends, is TSA = 2πr(r + h) = 2 × π × 3.8 × (3.8 + 11) = 112.48π ≈ 353.37 cm². Each circular end is πr² = 14.44π ≈ 45.36 cm², and 262.64 + 2 × 45.36 = 353.36, which agrees once rounding is allowed for.
The volume is πr²h = π × 3.8² × 11 = 158.84π ≈ 499.01 cm³, or just under half a litre. That is the geometric volume of the cylinder; the food inside is less, because of the rims and the headspace left when the tin is sealed.
Formulas and scoring rules
- Cube (edge a)
TSA = 6a²; LSA = 4a²; V = a³- Cuboid (length l, width w, height h)
TSA = 2(lw + lh + wh); LSA = 2h(l + w); V = lwh- Cylinder (radius r, height h)
TSA = 2πr(r + h); CSA = 2πrh; V = πr²h- Sphere (radius r)
TSA = 4πr²; V = (4/3)πr³- Hemisphere, solid (radius r)
TSA = 3πr²; CSA = 2πr²; V = (2/3)πr³- Cone (radius r, height h, slant l)
l = √(r² + h²); TSA = πr(r + l); CSA = πrl; V = (1/3)πr²hGiven the slant height instead, h = √(l² − r²); the slant must be longer than the radius.- Square prism (base side a, height h)
TSA = 2a² + 4ah; LSA = 4ah; V = a²h- Triangular prism (sides a, b, c, length L)
A = √(p(p − a)(p − b)(p − c)), p = (a + b + c)/2; TSA = 2A + (a + b + c)L; LSA = (a + b + c)L; V = ALHeron's formula; any three sides that satisfy the triangle inequality.- Square pyramid (base side a, height h)
s = √(h² + (a/2)²); TSA = a² + 2as; LSA = 2as; V = a²h/3s is the slant height of a triangular face, measured up the middle of the face.- Rounding
pi = Math.PI (15+ significant digits); results rounded half away from zero to the chosen decimal placesAnswers worked with π = 3.14 or 22/7 differ in the third or fourth significant figure.
Radius, diameter, height and slant height
Most mistakes with round shapes come from using the diameter where the formula needs the radius. Measure straight across the widest part of the circle and halve it. For a cone or pyramid, the vertical height runs from the tip straight down to the centre of the base, while the slant height runs down the sloping surface. The two are linked by Pythagoras, and the calculator works out whichever one you did not give.
For real objects, measure the outside if you want the material or paint needed and the inside if you want the capacity. A thick-walled pot has a noticeably larger outside area than inside.
Why the textbook answer can be slightly different
School books often use π = 22/7 or 3.14 so that sums come out neatly. A cone with radius 7 cm and height 24 cm has slant height 25 cm and curved area πrl = 175π: exactly 550 cm² with 22/7, 549.5 cm² with 3.14, and 549.78 cm² with the true value. If your book's answer is 550, the method is the same; only the value of π differs.
Limitations: what the result does not prove
- The shapes are ideal geometric solids. Rounded edges, lips, seams, overlaps for glue and the thickness of the material are not included, so add an allowance when cutting or ordering real material.
- Only right, regular versions are covered: the cone and pyramid have their tip above the centre of the base, and the prisms have their sides at right angles to the ends. Oblique shapes have the same volume but a different surface area.
- The capacity in litres is the geometric volume of the solid. A container's usable capacity is smaller because of wall thickness and the space left at the top.
- Shapes not listed here, such as a frustum, a torus or a rectangular-based pyramid, are not calculated; combining two listed shapes and subtracting the shared face gives most composite solids.
Privacy: where your data goes
Everything you paste, type or drop is processed in this browser tab. It is not uploaded, logged, stored or sent to analytics. Session recording and tag-manager scripts are switched off on this page.
Standards and sources
- NIST SP 811 - Guide for the Use of the International System of Units - checked 19 Sep 2026
- Wolfram MathWorld - Surface Area
- Wolfram MathWorld - Heron's Formula
Frequently asked questions
What is the formula for the surface area of a cylinder?
The total surface area is 2πr(r + h), which is the curved side 2πrh plus the two circular ends πr² each. For radius 3 cm and height 5 cm that is 2 × π × 3 × 8 = 48π, about 150.80 cm². Use 2πrh alone if the ends are open, as with a pipe or a label.
What is the difference between lateral and total surface area?
Total surface area includes every face, top and bottom as well. Lateral surface area counts only the sides, leaving out the bases. For a box it is the four walls, for a cylinder or cone it is the curved part, which is then usually called the curved surface area.
How do I find the surface area of a cone with only the radius and height?
Find the slant height first with Pythagoras, l = √(r² + h²), then use πr(r + l) for the total or πrl for the curved part. A cone of radius 3 and height 4 has slant 5, so its total area is π × 3 × 8 = 24π, about 75.40 square units.
Is the surface area of a hemisphere 2πr² or 3πr²?
Both, depending on the object. The curved dome alone is half a sphere, 2πr². A solid hemisphere also has a flat circular base of πr², giving 3πr² in total. A bowl uses 2πr²; a half-ball paperweight uses 3πr².
How do I calculate the surface area of a triangular prism?
Add the two triangular ends to the three rectangular sides: 2A + (a + b + c) × L, where A is the triangle's area and L the prism's length. With sides 3, 4 and 5 and length 10, A is 6, so the total is 12 + 12 × 10 = 132 square units.
Why do surface area and volume use different units?
Area measures a flat covering, so it is length times length, in square units such as cm² or ft². Volume measures space, length times length times length, in cubic units such as cm³ or m³. Converting needs the factor squared or cubed: 1 m² is 10,000 cm², and 1 m³ is 1,000,000 cm³.
How much paint do I need for a cylindrical tank?
Work out the area you will actually paint - usually the curved side 2πrh plus the top πr², not the base - then divide by the coverage on the tin, typically given in square metres per litre for one coat, and multiply by the number of coats. Measure the outside of the tank in metres so the area comes out in m².
Last reviewed by the A2Z.Tools team against the sources listed above.
