Basic solids
- Cube and rectangular cuboid
- Sphere and hemisphere
- Cylinder
- Cone
- Truncated cone (conical frustum)
Free geometry tool
Universal Surface Area Calculator
Calculate the area of a flat shape, the total surface area of a three-dimensional solid, or the combined area of a custom surface. Choose a formula-based shape, enter polygon coordinates, or build a surface from several regions.
Important: no single formula can calculate every possible surface
from incomplete measurements. This calculator covers many standard shapes and
lets you calculate irregular polygon areas or combine known surface regions.
For arbitrary curved or scanned surfaces, an appropriate geometric model or mesh
approximation is needed.
Calculate any supported area or surface
Select a calculation type and shape. All entered lengths are converted to metres internally, then the result is displayed in your chosen area unit.
Calculations are performed in your browser. Do not use rounded display
values as a substitute for the original measurements in engineering,
manufacturing, or construction work.
Flat 2D shapes supported
Use the 2D area mode for a flat region. These results represent planar area, not the exterior area of a 3D object.
Three-dimensional solids supported
Total surface area is the sum of the outside faces and curved surfaces of a solid. The calculator also displays volume where the selected shape has a supported volume formula.
Prisms and pyramids
- Right triangular prism
- Regular prism with a regular polygon base
- Regular square pyramid
- Square-pyramid frustum
For prisms, pyramids, and frustums, the formulas assume the specific geometry stated in the field labels. General skew solids may require face-by-face calculations instead.
Calculate an irregular or composite surface
Irregular polygon from coordinates
If you know the boundary vertices of a flat irregular polygon, enter their coordinates in order. The calculator applies the shoelace formula. This works for many concave polygons as long as the boundary does not intersect itself.
A = ½ × |Σ(xᵢyᵢ₊₁ − yᵢxᵢ₊₁)|
For a curved or very detailed outline, approximate the boundary with enough vertices. Smaller segments usually improve the approximation.
Combine multiple surface regions
If a surface can be divided into known regions, calculate each region separately and add their areas. Subtract holes or cutouts where appropriate.
Total area = sum of added regions − sum of cutouts
This method is useful for floor plans, panels, sheets, wall sections, composite outlines, and surfaces made of separate planar faces.
Do not subtract overlapping areas twice. For a 3D object's exterior, count only exposed faces; shared internal faces are not part of the exterior surface area.
Common area and surface area formulas
| Shape | Area or total surface area | Required measurements |
|---|---|---|
| Rectangle | A = lw | Length and width |
| Triangle | A = ½bh | Base and perpendicular height |
| Circle | A = πr² | Radius |
| Ellipse | A = πab | Semi-major and semi-minor axes |
| Trapezoid | A = ½(a + b)h | Parallel sides and perpendicular height |
| Regular polygon | A = ns² / (4 tan(π/n)) | Side length and number of sides |
| Cube | SA = 6a² | Edge length |
| Rectangular cuboid | SA = 2(lw + lh + wh) | Length, width, height |
| Sphere | SA = 4πr² | Radius |
| Cylinder | SA = 2πr² + 2πrh | Radius and perpendicular height |
| Cone | SA = πr² + πrℓ | Radius and slant height |
| Hemisphere | SA = 3πr² | Radius, including the flat base |
| Conical frustum | SA = π(R² + r²) + π(R + r)ℓ | Two radii and slant height |
Here, A means planar area, SA means total surface area, l is length, w is width, h is perpendicular height, r is radius, R is the larger radius, ℓ is slant height, and n is the number of sides.
Area unit conversions
| Unit | Equivalent in square metres |
|---|---|
| 1 mm² | 0.000001 m² |
| 1 cm² | 0.0001 m² |
| 1 m² | 1 m² |
| 1 km² | 1,000,000 m² |
| 1 in² | 0.00064516 m² |
| 1 ft² | 0.09290304 m² |
| 1 yd² | 0.83612736 m² |
Frequently asked questions
What is the difference between area and surface area?
Area usually refers to a flat two-dimensional region. Surface area is the combined area of the exterior faces or curved surfaces of a three-dimensional object.
Can this calculator calculate any shape?
It supports many standard shapes, arbitrary simple polygons from coordinates, and custom sums of known regions. An arbitrary shape cannot always be calculated exactly without sufficient dimensions, a boundary description, or a suitable mathematical model.
How do I calculate an irregular polygon?
Enter its vertices in boundary order as x,y coordinates. The calculator uses the shoelace formula to find the polygon's area. Avoid crossing boundaries and use a consistent coordinate unit.
How do I calculate a composite surface?
Divide the surface into regions whose areas you know, add those areas, and subtract holes or cutouts. For a 3D exterior, include only exposed faces and do not count shared internal faces.
Does the calculator support different units?
Yes. Lengths can be entered in millimetres, centimetres, metres, kilometres, inches, feet, or yards. Results are available in square millimetres, square centimetres, square metres, square kilometres, square inches, square feet, and square yards.
What is the difference between height and slant height?
Perpendicular height is measured at a right angle to the base. Slant height follows a sloping side or face. They are not interchangeable in cone and pyramid surface area formulas.
More geometry calculators
Universal area calculator
Calculate the planar area of common two-dimensional shapes.
Triangle area calculator
Calculate triangle area from base and height or other supported measurements.
Circle area calculator
Calculate circle area from its radius or diameter.
Rectangle area calculator
Calculate rectangle area from length and width.