Area Calculator

What this tool does

Pick a shape and enter its dimensions to get the area instantly, plus the perimeter or circumference when it can be derived from the inputs you gave. Every result shows the exact formula and substituted numbers so you can follow the working, not just copy an answer.

Geometry homework, flooring quotes and garden plans all boil down to the same question: how much surface does this shape cover? This calculator covers eight shapes you will meet constantly — four-sided figures, circles, triangles and sectors — and returns both the area and whichever boundary measurement (perimeter or circumference) makes sense for the data you supplied.

Rather than memorizing eight separate formulas, pick the shape from the dropdown and only the fields that formula needs will appear. The working shown underneath each answer spells out the formula with your own numbers plugged in, which doubles as a check against a textbook or a quick way to spot a typo in your input.

How to use Area Calculator

1. Choose the shape you are measuring from the Shape dropdown.
2. Fill in only the dimension fields that appear — unrelated fields for other shapes stay hidden.
3. Read the Area result, which updates live as you type.
4. Check the second result for perimeter or circumference, where the shape allows it to be calculated from the given inputs.
5. Expand the working note to see the formula with your values substituted in.
6. Switch shapes any time; your entered numbers for other shapes are remembered.

Tips for better results

• For a triangle given only base and height, the perimeter cannot be found — you would need the two slanted side lengths too, which is exactly what the Triangle Solver tool is built for.
• The ellipse perimeter uses Ramanujan’s well-known approximation because no exact elementary formula exists; it stays accurate to a tiny fraction of a percent for any ratio of axes.
• For a circular sector, keep the angle in degrees between 0 and 360 — the tool converts to radians internally before applying the area formula.
• Enter the parallelogram’s slanted side only if you also want the perimeter; area only needs the base and height.
• Keep units consistent across every field for a shape (all in centimeters, all in feet, etc.) since the tool has no unit conversion built in.

Common use cases

• Estimating how much paint, turf or flooring is needed to cover a room, yard or shape of known dimensions.
• Checking geometry homework answers for area and perimeter problems across common shapes.
• Sizing a circular or sector-shaped garden bed, pizza slice or pie chart segment by area.
• Comparing material cost per square unit between shape options for a design or construction project.

Common mistakes to avoid

• Mixing up radius and diameter for circles, sectors and spheres-related area problems — this tool always expects the radius.
• Entering the sector angle in radians instead of degrees, which produces a wildly wrong area.
• Expecting a perimeter for a triangle or trapezoid when only base and height were given — those shapes need additional side lengths that this shortcut does not collect.
• Forgetting that semi-major and semi-minor axis for an ellipse are half the full width and height, not the full width and height themselves.