Find the surface area to volume ratio
How to calculate the surface area to volume ratio: pick a shape and type its sides or radius. The surface area to volume ratio calculator gives SA:V with the surface area, the volume and the steps.
- Surface area to volume ratio
- 3 : 1 (3 per cm)
The surface area to volume ratio is 3 : 1 (3 per cm).
- Surface area to volume ratio (per unit of length)
- 3
- Surface area (unit²)
- 24
- Volume (unit³)
- 8
- Steps
- Surface area = 6a² = 6 × 2² = 24 cm²; Volume = a³ = 2³ = 8 cm³; Ratio = 6 ÷ a = 6 ÷ 2 = 3 per cm
Surface area to volume ratio: 3 : 1 (3 per cm). The surface area to volume ratio is 3 : 1 (3 per cm).
How it is worked out
How to calculate
Finds the surface area, the volume and the surface area to volume ratio (SA:V) of a cube, a sphere, a cylinder or a rectangular box, with the steps.
Example with the default inputs (Shape Cube, Side (a) 2, Length unit cm): The surface area to volume ratio is 3 : 1 (3 per cm).
Method: Cube: SA = 6a², V = a³, SA:V = 6 ÷ a. Sphere: SA = 4πr², V = 4/3 πr³, SA:V = 3 ÷ r. Cylinder: SA = 2πr² + 2πrh, V = πr²h, SA:V = 2(r + h) ÷ (rh). Box: SA = 2(lw + lh + wh), V = lwh.
- All lengths are in the same unit; the ratio is per that unit of length, so it changes when the unit changes.
- Typed lengths are read as the exact decimals you typed.
Worked examples
Each example is checked against the calculator on every build.
- Shape Cube, Side (a) 1, Length unit mm gives Surface area (unit²) 6, Volume (unit³) 1, Surface area to volume ratio (per unit of length) 6, Surface area to volume ratio 6 : 1 (6 per mm).Source: OpenStax, Biology 2e, §4.2 Prokaryotic Cells (Cell Size: a sphere’s surface area is 4πr² and its volume 4πr³/3; Figure 4.7: cells of 1 mm³ and 6 mm² and of 8 mm³ and 24 mm² have surface area to volume ratios of 6 to 1 and 3 to 1), https://openstax.org/books/biology-2e/pages/4-2-prokaryotic-cells (retrieved 2026-10-19); OpenStax, Prealgebra 2e, §9.6 Solve Geometry Applications: Volume and Surface Area (rectangular solid V = LWH, S = 2LH + 2LW + 2WH; cube V = s³, S = 6s²; sphere V = 4/3 πr³, S = 4πr²; cylinder V = πr²h, S = 2πr² + 2πrh), https://openstax.org/books/prealgebra-2e/pages/9-6-solve-geometry-applications-volume-and-surface-area (retrieved 2026-10-19)
- Shape Cube, Side (a) 2, Length unit mm gives Surface area (unit²) 24, Volume (unit³) 8, Surface area to volume ratio (per unit of length) 3, Steps Surface area = 6a² = 6 × 2² = 24 mm²; Volume = a³ = 2³ = 8 mm³; Ratio = 6 ÷ a = 6 ÷ 2 = 3 per mm.Source: OpenStax, Biology 2e, §4.2 Prokaryotic Cells (Cell Size: a sphere’s surface area is 4πr² and its volume 4πr³/3; Figure 4.7: cells of 1 mm³ and 6 mm² and of 8 mm³ and 24 mm² have surface area to volume ratios of 6 to 1 and 3 to 1), https://openstax.org/books/biology-2e/pages/4-2-prokaryotic-cells (retrieved 2026-10-19); OpenStax, Prealgebra 2e, §9.6 Solve Geometry Applications: Volume and Surface Area (rectangular solid V = LWH, S = 2LH + 2LW + 2WH; cube V = s³, S = 6s²; sphere V = 4/3 πr³, S = 4πr²; cylinder V = πr²h, S = 2πr² + 2πrh), https://openstax.org/books/prealgebra-2e/pages/9-6-solve-geometry-applications-volume-and-surface-area (retrieved 2026-10-19)
- Shape Cube, Side (a) 2.5, Length unit in gives Surface area (unit²) 37.5, Volume (unit³) 15.625, Surface area to volume ratio (per unit of length) 2.4.Source: OpenStax, Prealgebra 2e, §9.6 Solve Geometry Applications: Volume and Surface Area (rectangular solid V = LWH, S = 2LH + 2LW + 2WH; cube V = s³, S = 6s²; sphere V = 4/3 πr³, S = 4πr²; cylinder V = πr²h, S = 2πr² + 2πrh), https://openstax.org/books/prealgebra-2e/pages/9-6-solve-geometry-applications-volume-and-surface-area (retrieved 2026-10-19)
- Shape Sphere, Radius (r) 3, Length unit µm gives Surface area (unit²) 113.097, Volume (unit³) 113.097, Surface area to volume ratio (per unit of length) 1, Surface area to volume ratio 1 : 1 (1 per µm).Source: OpenStax, Biology 2e, §4.2 Prokaryotic Cells (Cell Size: a sphere’s surface area is 4πr² and its volume 4πr³/3; Figure 4.7: cells of 1 mm³ and 6 mm² and of 8 mm³ and 24 mm² have surface area to volume ratios of 6 to 1 and 3 to 1), https://openstax.org/books/biology-2e/pages/4-2-prokaryotic-cells (retrieved 2026-10-19)
- Shape Cylinder, Radius (r) 1, Height (h) 2, Length unit cm gives Surface area (unit²) 18.8496, Volume (unit³) 6.28319, Surface area to volume ratio (per unit of length) 3.Source: OpenStax, Prealgebra 2e, §9.6 Solve Geometry Applications: Volume and Surface Area (rectangular solid V = LWH, S = 2LH + 2LW + 2WH; cube V = s³, S = 6s²; sphere V = 4/3 πr³, S = 4πr²; cylinder V = πr²h, S = 2πr² + 2πrh), https://openstax.org/books/prealgebra-2e/pages/9-6-solve-geometry-applications-volume-and-surface-area (retrieved 2026-10-19)
- Shape Box, Length (l) 3, Width (w) 2, Height (h) 1, Length unit in gives Surface area (unit²) 22, Volume (unit³) 6, Surface area to volume ratio (per unit of length) 3.66667, Surface area to volume ratio 3.66667 : 1 (3.66667 per in).Source: OpenStax, Prealgebra 2e, §9.6 Solve Geometry Applications: Volume and Surface Area (rectangular solid V = LWH, S = 2LH + 2LW + 2WH; cube V = s³, S = 6s²; sphere V = 4/3 πr³, S = 4πr²; cylinder V = πr²h, S = 2πr² + 2πrh), https://openstax.org/books/prealgebra-2e/pages/9-6-solve-geometry-applications-volume-and-surface-area (retrieved 2026-10-19)
How it works
The surface area to volume ratio is SA:V = surface area ÷ volume. Pick a shape and type its lengths, all in one unit:
| Shape | Surface area | Volume | SA:V |
|---|---|---|---|
| Cube, side a | 6a² | a³ | 6 ÷ a |
| Sphere, radius r | 4πr² | 4/3 πr³ | 3 ÷ r |
| Cylinder, radius r and height h | 2πr² + 2πrh = 2πr(r + h) | πr²h | 2(r + h) ÷ (rh) |
| Box, length l, width w, height h | 2(lw + lh + wh) | lwh | 2(lw + lh + wh) ÷ (lwh) |
The ratio has the unit 1 ÷ length: the page writes it as a ratio to 1 and per unit, R : 1 (R per u), where u is the unit you chose (µm, mm, cm, m, in or ft). The area is in u² and the volume in u³. The unit is a label only: the numbers are the same whichever unit you pick.
Steps. The page lists three steps, separated by semicolons. For a cube: Surface area = 6a² = 6 × a² = A u²; Volume = a³ = a³ = V u³; Ratio = 6 ÷ a = 6 ÷ a = R per u, with the typed side and the results written as numbers. A sphere writes 4πr² = 4π × r², 4/3 πr³ = 4/3 π × r³ and 3 ÷ r = 3 ÷ r; a cylinder 2πr² + 2πrh = 2π × r × (r + h), πr²h = π × r² × h and 2(r + h) ÷ (rh) = 2 × (r + h) ÷ (r × h); a box 2(lw + lh + wh) = 2 × (l × w + l × h + w × h), lwh = l × w × h and SA ÷ V. The full lines are in the worked examples below.
Rules
- Each length is from 10⁻⁹ to 10⁹, in the unit chosen, and the limits include their ends.
Output format
Every number, in the answer, the steps and the outputs, shows to 6 significant figures, rounded half up, with trailing zeros dropped, thousands commas, and from 10¹⁵ up or below 10⁻⁶ as a × 10ⁿ. Typed lengths are read as the exact decimals you typed: the ratio is an exact fraction rounded once (π cancels for the sphere and the cylinder), as are a cube's and a box's area and volume; a sphere's or a cylinder's area and volume are an exact fraction times π, a 64-bit float.
The answer sentence reads The surface area to volume ratio is R : 1 (R per u).
Worked examples by hand
Cells as cubes (OpenStax Biology 2e Figure 4.7). A 1 mm cube: SA = 6 × 1² = 6 mm², V = 1³ = 1 mm³, SA:V = 6 : 1 (6 per mm). A 2 mm cube: Surface area = 6a² = 6 × 2² = 24 mm²; Volume = a³ = 2³ = 8 mm³; Ratio = 6 ÷ a = 6 ÷ 2 = 3 per mm, so SA:V = 3 : 1.
A 2.5 in cube (OpenStax Prealgebra 2e Example 9.49). SA = 6 × 2.5² = 37.5 in², V = 2.5³ = 15.625 in³, SA:V = 37.5 ÷ 15.625 = 2.4 per in.
A round cell. Radius 3 µm: SA = 4π × 3² = 36π = 113.097 µm², V = 4/3 π × 3³ = 36π = 113.097 µm³, SA:V = 3 ÷ 3 = 1 : 1 (1 per µm).
A cylinder. r = 1 cm, h = 2 cm: SA = 2π × 1 × (1 + 2) = 6π = 18.8496 cm², V = π × 1² × 2 = 2π = 6.28319 cm³, SA:V = 2 × (1 + 2) ÷ (1 × 2) = 3 per cm.
A box. 3 × 2 × 1 in: SA = 2 × (3 × 2 + 3 × 1 + 2 × 1) = 22 in², V = 3 × 2 × 1 = 6 in³, SA:V = 22 ÷ 6 = 3.66667 : 1 (3.66667 per in).
Other questions people ask
How do you calculate the surface area to volume ratio?
Work out the surface area and the volume, then divide: SA:V = surface area ÷ volume. A cube with 2 mm sides has 6 × 2² = 24 mm² and 2³ = 8 mm³, so SA:V = 24 ÷ 8 = 3, written 3 : 1.
What is the surface area to volume ratio of a sphere?
SA:V = 4πr² ÷ (4/3 πr³) = 3 ÷ r: π cancels. A cell of radius 3 µm has SA:V = 1 per µm; at radius 1 µm it is 3 per µm.
Why does the ratio fall as a cell gets bigger?
Area grows with the square of the size and volume with the cube (OpenStax Biology 2e §4.2). Double a cube’s side and its area grows 4 times but its volume 8 times, so SA:V halves: 6 : 1 at 1 mm, 3 : 1 at 2 mm.
Why does a high surface area to volume ratio matter for cells?
A cell takes in food and gets rid of waste through its surface, but its needs grow with its volume. A small cell has more surface for each unit of volume, which is one reason cells stay small or divide.
Does the unit change the ratio?
Yes. SA:V has the unit 1 ÷ length: a 1 cm cube has 6 per cm, which is 0.6 per mm. Keep every length in one unit and read the ratio per that unit.
What is the ratio for a cylinder?
SA = 2πr² + 2πrh and V = πr²h, so SA:V = 2(r + h) ÷ (rh). A cylinder of radius 1 cm and height 2 cm has 2 × 3 ÷ 2 = 3 per cm.