The formula this page uses
a² + b² = c² Area of a triangle = ½ · base · height Area of a circle = π r²
Geometry Calculator
Solve geometry problems with clear steps, notation, and a final check. Choose a focused operation below to calculate, inspect the method, and connect the result to a visual model.
The visual updates with your calculation.
Result—Choose a mode, enter the known values, and calculate.
Show your work Step-by-step method
- The calculation method and verification will appear here.
Geometry
Geometry Calculator explained
The short version
- Perimeter adds lengths, area multiplies two perpendicular lengths, and volume multiplies three.
- Get the units right and half the marks look after themselves: cm for perimeter, cm² for area, cm³ for volume.
- In a right triangle the two short sides squared always add up to the long side squared.
What each part means
SymbolWhat it means
a, b — The two legsThe sides that meet at the right angle, in the same length unit.
c — The hypotenuseThe side opposite the right angle. It is always the longest side.
h — Perpendicular heightThe straight-down distance from the top vertex to the base line, not a slanted side.
r — RadiusCentre to edge of a circle. Half the diameter.
Show your work: a full example
- A right-angled garden bed with legs 9 m and 12 ma = 9 m, b = 12 m
- Square both legs and add9² + 12² = 81 + 144 = 225
- Take the square rootc = √225 = 15 m
- Add the three sides for the fence9 + 12 + 15 = 36 m
- The legs meet at a right angle, so they are base and height½ × 9 × 12 = ½ × 108
- Finish the area54 m²
- Check the units36 m of fencing, 54 m² of soil — length in m, area in m²
A second, different case
- A different case: a 72° slice of a circle with radius 5 cmr = 5 cm, angle = 72°
- Area of the whole circleπ × 5² = 25π ≈ 78.54 cm²
- What fraction of the circle the slice is72 ÷ 360 = 0.2
- Area of the slice0.2 × 25π = 5π ≈ 15.71 cm²
- Circumference of the whole circle2π × 5 = 10π ≈ 31.42 cm
- Curved edge of the slice0.2 × 10π = 2π ≈ 6.28 cm
- Perimeter of the slice, curve plus two radii6.28 + 5 + 5 = 16.28 cm
Copy-ready example
a = 9 m, b = 12 m
A right-angled garden bed with legs 9 m and 12 m
Questions about the Geometry Calculator
When am I allowed to use a² + b² = c²?
Only in a triangle that has a 90° angle, and only with c as the side facing that angle. In the 9-12-15 triangle above, writing 9² + 15² = 12² would be wrong because 15 is the hypotenuse, not a leg.
Why is area measured in square units but volume in cubic units?
Area counts how many 1×1 tiles cover a surface, so each unit is a length times a length: m × m = m². Volume counts 1×1×1 boxes, which is three lengths multiplied, giving m³.
Should I leave π in my answer or type 3.14?
Leave it as 5π when the question says exact form, because 5π is the true value and 15.71 is rounded. Switch to a decimal only when you need to measure, compare or add it to a number that is already a decimal.
How do I find the height of a triangle that has no right angle?
Drop a perpendicular from the top vertex straight down to the base line, extending the base if you have to, and measure that segment. If you only know the three sides, Heron's formula gives the area without ever finding the height.
Calculate, interpret, verify.
This workspace keeps the formula and the meaning together. Decimal results are rounded for display; retain full precision when you continue a calculation.
Enter known values
Match each input to the quantities in the problem and keep units consistent.
Use the relationship
The result panel identifies the formula or algorithm and shows the main substitutions.
Read the visual
Use the diagram, plot, or data display to check scale, direction, and plausibility.
Practice unaided
Move to targeted questions once you can explain why the method applies.
Learn the mathematics
Understand geometry behind this calculator
A calculator confirms an answer. Working the method yourself is what makes the next problem faster.