23 free geometry calculators for shapes, areas, volumes, and coordinate geometry.
| Group | Calculators |
|---|---|
| General | Area · Perimeter · Surface Area · Volume |
| Triangles | Right Triangle · Triangle · Pythagorean Theorem |
| Quadrilaterals | Square · Rectangle · Parallelogram · Rhombus · Trapezoid · Kite |
| Circles and curves | Circle · Ellipse · Arc Length · Sector · Chord Length · Circular Segment · Annulus |
| Polygons | Regular Polygon |
| Coordinate geometry | Distance Between Points · Slope |
Confusing these is the most common geometry error, and it has real cost when you are ordering materials.
| Measure | Describes | Units | You order this way for |
|---|---|---|---|
| Perimeter | The distance around an edge | m | Fencing, skirting, edging, cornice |
| Area | The surface covered | m² | Paint, tiles, turf, flooring, plasterboard |
| Volume | The space filled | m³ | Concrete, soil, mulch, water, excavation |
The units tell you which one you need. If a supplier quotes per metre you want perimeter, per square metre you want area, per cubic metre you want volume. Concrete and soil are always sold by the cubic metre in Australia, and a common expensive mistake is calculating a slab's area in m² and ordering that many cubic metres — for a 100 m² slab at 100 mm thick, that is 100 m³ ordered against 10 m³ needed.
This catches people out constantly and is worth internalising.
Double the length → perimeter ×2 · area ×4 · volume ×8
A room twice as long and twice as wide needs four times the flooring, not twice. A water tank with double the dimensions holds eight times the water. This is why a 3,000-litre tank is not physically twice a 1,500-litre one, and why paint estimates scale faster than people expect when a plan grows.
A quick sanity check for any building estimate. Work out roughly what the answer should be before you calculate. A standard Australian bedroom is around 12 m². A single garage is about 18 m². A concrete path 1 m wide and 10 m long at 100 mm deep is 1 m³. If your calculated figure is ten times any of these, you have probably mixed up your units — and it is far cheaper to catch that before ordering than after delivery.
The theorem is a school formula that trades use daily, usually without naming it.
a² + b² = c² (right-angled triangles only)
The 3-4-5 rule is the practical version: measure 3 m along one edge, 4 m along the other, and if the diagonal between those points is exactly 5 m, the corner is square. Any multiple works — 1.5-2-2.5 for small work, 6-8-10 for a house slab. Bigger triangles give better accuracy, because a small angular error shows up as a larger distance error over a longer run.
Check the diagonals before you pour. On a rectangular slab or deck frame, both diagonals should measure the same. If they differ, the frame is a parallelogram rather than a rectangle, and every subsequent measurement inherits the error. It takes a minute to check and is very difficult to fix afterwards.
| Shape | Is | Example |
|---|---|---|
| Circle | The whole shape | A round tabletop |
| Sector | A wedge from the centre | A slice of pizza |
| Segment | The piece cut off by a straight chord | The top sliced off a round cake |
| Arc | Part of the edge itself | A curved garden border |
| Chord | A straight line between two points on the edge | A straight path across a round lawn |
Sectors and segments are frequently mixed up. A sector is bounded by two radii and an arc — it reaches the centre. A segment is bounded by a chord and an arc, and does not. Partly filled cylindrical tanks are a segment problem, which is why a horizontal tank half full by depth is not half full by volume.
1. Mixing units mid-calculation. Convert millimetres to metres before you start, not after.
2. Ordering area when you need volume. Depth is the difference, and it is usually the expensive one.
3. Using Pythagoras on a non-right triangle. It only applies where there is a 90° angle.
4. Assuming doubling dimensions doubles the answer. Area goes up four times, volume eight.
5. Forgetting waste allowance. Tiles and flooring typically need 5–10% extra for cuts and breakage.
6. Confusing radius and diameter. Halving one of them halves your radius and quarters your area.
Geometry calculators give you the raw quantity. Turning that into an order usually needs a waste allowance, a delivery minimum, and sometimes a different unit than you calculated in.
Our building calculators handle several of those conversions directly — concrete volume, paint coverage, decking and fencing — with Australian material assumptions built in. For unit conversion between metric and imperial, the unit converter covers length, area and volume.
Australian Building Codes Board — National Construction Code · Standards Australia · OpenStax — Mathematics (open textbooks)