Area Calculator
Choose a shape, enter its dimensions and get the area and, where the dimensions fix it, the perimeter. Covers the rectangle, triangle, trapezoid
Try your own numbers
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 area and perimeter from shape, 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 floor area of a plant room, the area of a panel, a trench cross-section, a solar array footprint, the area of a tapered duct or cable trench, or the face of a hexagonal nut. For a circle use the circle calculator, and for a triangle from its three sides use the triangle calculator. For volumes and surface areas of solids use the volume and surface area calculator.
Cross-check: 48 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 | 48 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 |
|---|---|
| Shape | Rectangle |
| First dimension | 6 |
| Second dimension | 4 |
- Area = length × width = 6 × 4 = 24
- Perimeter = 2 (length + width) = 20
Assumptions
- Every dimension is in one consistent unit, and the area is in that unit squared: metres give square metres, millimetres give square millimetres
- The perimeter is shown for the rectangle, ellipse, sector, ring and regular polygon, where the dimensions fix it. The triangle, trapezoid and parallelogram need their slanted sides, which are not entered, so the perimeter shows a dash; for a triangle with three known sides use the triangle calculator
- The ellipse perimeter has no simple closed form; it is found with the arithmetic-geometric mean method and is accurate to many digits. The ring perimeter is both circles added together. The sector perimeter is the two radii plus the arc
- Dimensions the chosen shape does not use are ignored and a note says so
- The tool works on plain numbers and does not track units
Use this to find the floor area of a plant room, the area of a panel, a trench cross-section, a solar array footprint, the area of a tapered duct or cable trench, or the face of a hexagonal nut. For a circle use the circle calculator, and for a triangle from its three sides use the triangle calculator. For volumes and surface areas of solids use the volume and surface area calculator.
Inputs and results
| Input | Unit | Allowed or shown | Note |
|---|---|---|---|
| Shape | (choice) | Rectangle; Triangle (base and height); Trapezoid; Parallelogram; Ellipse; Circular sector; Ring (annulus); Regular polygon | |
| First dimension | (number) | 0 or more, up to 1,000,000,000,000 | Rectangle: length. Triangle: base. Trapezoid: first parallel side. Parallelogram: base. Ellipse: semi-axis a (half the long width). Sector: radius. Ring: outer radius. Polygon: number of sides (a whole number from 3 to 1000). |
| Second dimension | (number) | 0 or more, up to 1,000,000,000,000; may be left blank | Rectangle: width. Triangle: height. Trapezoid: second parallel side. Parallelogram: height. Ellipse: semi-axis b. Sector: angle in degrees (up to 360). Ring: inner radius. Polygon: length of one side. |
| Third dimension | (number) | 0 or more, up to 1,000,000,000,000; may be left blank | Used only by the trapezoid, where it is the height between the two parallel sides. Leave it blank for every other shape. |
| Result | Unit | Allowed or shown | Note |
|---|---|---|---|
| Area | (number) | Shown to 10 decimal places | |
| Perimeter (shown where the dimensions fix it) | (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 | Area | Perimeter |
|---|---|---|
| 0.6 | 2.4 | 9.2 |
| 1.5 | 6 | 11 |
| 3 | 12 | 14 |
| 6 | 24 | 20 |
| 12 | 48 | 32 |
| 24 | 96 | 56 |
| 60 | 240 | 128 |
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 shape, 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, and the area is in that unit squared: metres give square metres, millimetres give square millimetres. The perimeter is shown for the rectangle, ellipse, sector, ring and regular polygon, where the dimensions fix it. The triangle, trapezoid and parallelogram need their slanted sides, which are not entered, so the perimeter shows a dash; for a triangle with three known sides use the triangle calculator. The ellipse perimeter has no simple closed form; it is found with the arithmetic-geometric mean method and is accurate to many digits. The ring perimeter is both circles added together. The sector perimeter is the two radii plus the arc. Dimensions the chosen shape does not use are ignored and a note says so. The tool works on plain numbers and does not track units.
Which calculators should I use next?
Common next steps are Circle Calculator (Radius, Diameter, Circumference, Area), Triangle Calculator (Three Sides), Volume and Surface Area Calculator (Box, Cylinder, Sphere, Cone, Pipe) and Pythagorean Theorem (Right Triangle) Calculator. 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. 48 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.
- Conduit Fill Formulas: Percent Fill and Size: Conduit fill formulas: cable area from diameter, percent fill, the smallest conduit for a set of cables
- Cable Tray Fill Formulas: Area and Cable Count: Cable tray fill formulas: cable area from diameter, tray cross-section area
- Conductor Resistance Formulas and Temperature: Conductor resistance formulas: resistance from length, area and resistivity, correction for temperature
More Engineering Mathematics calculatorsAll engineering calculatorsArea Calculator (Rectangle, Trapezoid, Ellipse, Sector, Ring, Polygon) in Elecmetric