Volume and Surface Area Calculator
Choose a solid, enter its dimensions and get the volume, the total surface area and the curved or side surface area. Covers the box, cylinder, sphere
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Estimate only. Not engineering or safety advice. Check the result against the applicable standard and the equipment data, and have a competent engineer review it before it is relied on. Terms of use.
Open in the calculator with these values
About this calculator
This page calculates volume, total surface area and curved or side surface area from solid, first dimension, second dimension and third dimension. Change any value or its unit and the result updates. The steps below show the working for the default values, so you can check each line against your own method.
Limits of this calculator
Use this to find the capacity of a cylindrical tank or sump, the volume of concrete in a round foundation or a rectangular pad, the volume of a cable drum or duct section, the material in a pipe wall, or the paint or coating area of a pipe, tank or pole. For a flat shape use the area calculator, and for conductor or pipe cross-sections use the circle calculator.
Cross-check: 36 reference cases, calculated from textbook formulas coded separately from the engine by the same author, agree with this calculator. This is not an independent review.
Verification status: Engineering reference
Engineering reference. Formula and method documented and tested against separately coded reference calculations. Not yet Verified: the evidence listed on this page is still needed.
What this calculator checks
- The arithmetic of the published formula for the values you entered, in the units shown.
What remains unverified
- That the inputs suit your application. Take ratings, resistances and constants from the manufacturer data sheet or project specification.
Verification register entry
| Calculation author | Rahul Sharma (author) |
|---|---|
| Technical review | No independent technical review has been carried out |
| Individual professional approval | Not recorded |
| Formula reference | not recorded |
| Standard and edition | Not applicable: Pure mathematics or statistics; no electrical standard governs the method |
| Standard review state | Not applicable |
| Scope-screening note | not recorded |
| Cross-check test cases | 36 reference vectors (tests/reference_vectors.json) |
| Review date | not recorded |
| Next review date | not recorded |
| Status | Engineering reference |
Needed before this calculator can be marked Verified: reviewer name, qualification and review date; exact formula reference; formula source (textbook or standard); next review date.
Formula
Worked example
| Input | Value |
|---|---|
| Solid | Cylinder |
| First dimension | 2 |
| Second dimension | 5 |
- Volume = π r² h = π × 2² × 5 = 62.8318530718
- Total surface area = 2π r (r + h) = 87.9645943005
- Curved area = 2π r h = 62.8318530718
Assumptions
- Every dimension is in one consistent unit; the volume is in that unit cubed and the surface area in that unit squared. Dimensions in metres give cubic metres, and one cubic metre is 1000 litres
- The box side area is the four vertical faces; the cylinder and cone curved areas leave out the flat ends; for a sphere the curved area is the whole surface
- The hollow cylinder (pipe) total surface counts the outer and inner curved surfaces and both ring-shaped ends; the volume is the material of the wall, not the bore
- Dimensions the chosen solid does not use are ignored and a note says so
- The tool works on plain numbers and does not track units; wall thickness is the outer radius minus the inner radius
Use this to find the capacity of a cylindrical tank or sump, the volume of concrete in a round foundation or a rectangular pad, the volume of a cable drum or duct section, the material in a pipe wall, or the paint or coating area of a pipe, tank or pole. For a flat shape use the area calculator, and for conductor or pipe cross-sections use the circle calculator.
Inputs and results
| Input | Unit | Allowed or shown | Note |
|---|---|---|---|
| Solid | (choice) | Box (cuboid); Cylinder; Sphere; Cone; Hollow cylinder (pipe) | |
| First dimension | (number) | 0 or more, up to 1,000,000,000,000 | Box: length. Cylinder: radius. Sphere: radius. Cone: radius of the base. Hollow cylinder: outer radius. |
| Second dimension | (number) | 0 or more, up to 1,000,000,000,000; may be left blank | Box: width. Cylinder: height. Cone: height. Hollow cylinder: inner radius. Leave it blank for a sphere. |
| Third dimension | (number) | 0 or more, up to 1,000,000,000,000; may be left blank | Box: height. Hollow cylinder: length. Leave it blank for the cylinder, sphere and cone. |
| Result | Unit | Allowed or shown | Note |
|---|---|---|---|
| Volume | (number) | Shown to 10 decimal places | |
| Total surface area | (number) | Shown to 10 decimal places | |
| Curved or side surface area (without the ends) | (number) | Shown to 10 decimal places |
How it is calculated
Each input is converted to the base unit of its quantity, the formula above is applied in the order shown in the worked example, and each result is shown in the unit you choose. Results are held at full precision and rounded only for display, except where a step selects a standard size, as the worked example shows. A value outside its allowed range is refused with a message instead of giving a result.
How the result changes with first dimension
| First dimension | Volume | Total surface area | Curved or side surface area |
|---|---|---|---|
| 0.2 | 0.6283185307 | 6.5345127195 | 6.2831853072 |
| 0.5 | 3.926990817 | 17.2787595947 | 15.7079632679 |
| 1 | 15.7079632679 | 37.6991118431 | 31.4159265359 |
| 2 | 62.8318530718 | 87.9645943005 | 62.8318530718 |
| 4 | 251.3274122872 | 226.1946710585 | 125.6637061436 |
| 8 | 1,005.3096491487 | 653.4512719467 | 251.3274122872 |
| 20 | 6,283.1853071796 | 3,141.5926535898 | 628.318530718 |
Other inputs are the same as in the worked example above.
Standards and further reading
Complex numbers, rectangular and polar form and angle conversion are standard mathematics, not the subject of a standard. Standards apply when the result feeds an electrical design, and they set the method there.
Frequently asked questions
What do I need to enter?
Enter solid, first dimension, second dimension and third dimension. Change the unit of a value with its selector and the result stays the same.
What does this calculator assume?
Every dimension is in one consistent unit; the volume is in that unit cubed and the surface area in that unit squared. Dimensions in metres give cubic metres, and one cubic metre is 1000 litres. The box side area is the four vertical faces; the cylinder and cone curved areas leave out the flat ends; for a sphere the curved area is the whole surface. The hollow cylinder (pipe) total surface counts the outer and inner curved surfaces and both ring-shaped ends; the volume is the material of the wall, not the bore. Dimensions the chosen solid does not use are ignored and a note says so. The tool works on plain numbers and does not track units; wall thickness is the outer radius minus the inner radius.
Which calculators should I use next?
Common next steps are Area Calculator (Rectangle, Trapezoid, Ellipse, Sector, Ring, Polygon), Circle Calculator (Radius, Diameter, Circumference, Area), Pythagorean Theorem (Right Triangle) Calculator and Triangle Calculator (Three Sides). The related links at the bottom of this page open them.
How accurate are the results?
Every figure comes from the same tested engine as the Elecmetric calculators and is meant for estimating. 36 reference cases, calculated from textbook formulas coded separately from the engine by the same author, agree with this calculator. This is not an independent review. Check design values against the standard and the equipment data you work to.
Formula guides and reference
Longer explanations with worked examples and tables, written for the same topic.
- Pneumatic Cylinder Force and Air Use: Air cylinder formulas: the extend and retract force from the pressure and the bore
- Compressor Power Formulas: Air compressor formulas: the isothermal power for a free air delivery and pressure ratio
- Hydraulic Power and Cylinder Force Formulas: Hydraulic formulas: the power from the flow and pressure
More Engineering Mathematics calculatorsAll engineering calculatorsVolume and Surface Area Calculator (Box, Cylinder, Sphere, Cone, Pipe) in Elecmetric