Area and Volume Calculator

Features

• 14 shapes: rectangle, square, triangle (base and height, or three sides), circle, sector, trapezoid, parallelogram, rhombus, cube, cuboid, cylinder, cone, sphere
• The shape is drawn to scale from what you type — the proportions match the numbers
• Area and perimeter for flat shapes; volume, surface area, lateral area and base area for solids
• Derived values too: diameter, diagonal, slant height, arc length, chord length
• The formulas are listed in the output so you can check them by hand
• Three-sided triangles use Heron’s formula; sides that cannot close a triangle are reported as an error, not as NaN
• Quantities that cannot be determined (like the perimeter of a triangle given only its base and height) are omitted, with a note
• Units mm / cm / m / in, the same in and out
• Impossible dimensions are explained instead of leaving a plausible-looking drawing on screen

How to use

1. Choose a shape (eight flat ones first, then five solids)
2. Fill in the dimensions it asks for — only the relevant boxes appear
3. Switch the unit if you need to; the drawing and the numbers follow
4. Results are grouped into result, base and notes
5. Use the per-row copy button for a single value

FAQ

Why is there no perimeter for a triangle given only its base and height?

Because it is not determined. Once the base and the height are fixed, the third vertex can slide anywhere along a line parallel to the base, and the perimeter grows without bound. Rather than inventing a number, the tool drops that row and says why — use the three-side form to get a perimeter.

Is the drawing to scale?

Yes — it is drawn to scale, not sketched. A 6×4 rectangle comes out 3:2, and a cylinder with radius 2 and height 5 keeps that ratio between its ellipse and its height, so you can use the picture to spot a mistyped dimension. Three-sided triangles place the third vertex by the law of cosines, so the side lengths keep their true relationships.

Why is the base of a cylinder an ellipse?

Because that is what a circle looks like from an angle — the usual cabinet projection, with depth running at 45°. The visible half of the base is drawn solid; the half hidden by the cylinder is dashed or left out.

A sphere with r=3 gives 36π for both volume and surface area — is that a bug?

No, it is a coincidence of that radius. Volume is 4/3·πr³ (cubic units) and surface area is 4πr² (square units), so they only coincide at r=3. Double the radius and the volume goes up 8× while the surface area goes up 4×.

Why do the numbers not change when I switch units?

Because no conversion is done — only the suffix changes. Type 6 cm and the results come back in cm² and cm³. To convert yourself: when lengths differ by 10, areas differ by 100 and volumes by 1000.