Which formula fits my measured shape?
Use side lengths for a triangle or rectangle and radius for a circle. Verify shape constraints and squared area units first.
Plane geometry
Plane geometry
Calculate triangle, rectangle and circle areas, perimeters and dimensions. Check measurement units, shape constraints, formulas and reproducible examples.
3 calculatorsEnglish and ChineseNo account required
From question to result
Choose a path for your question
Calculate first, understand the formula and example, then compare your options. Each link answers a different question.
Calculator set
Plane geometry calculators
Open a calculator for an immediate estimate, then use its method notes, examples, limits, and sources to understand the result.
Triangle CalculatorFind a triangle’s area and perimeter from three sides using Heron’s formula. All sides must use the same length unit and satisfy the strict triangle inequality.CalculateRectangle CalculatorCalculate area, perimeter and diagonal from two perpendicular side lengths. These equations require a rectangle, not an arbitrary quadrilateral.CalculateCircle CalculatorCalculate radius, diameter, area and circumference from one known circle measurement. The selected measurement determines whether the input is a length or an area.Calculate
Understand, then calculate
Make sense of the key numbers in Plane geometry
Lengths, areas and perimeters have different dimensions. Doubling every side of a similar shape doubles its perimeter but multiplies its area by four. This gives a useful independent check: an area result should be reported in squared length units, never in the same unit as a radius or side length. Rectangle diagonals follow the Pythagorean theorem; circle circumference is proportional to radius, while circle area is proportional to the square of radius.
Not every three positive lengths form a triangle. The sum of the shorter two must strictly exceed the longest; equality describes a degenerate line with zero area rather than a usable triangle. Heron’s formula uses the semi-perimeter, not the perimeter, and its square-root expression is meaningful only after checking those side constraints. Measurements near degeneracy can magnify rounding error. Use the precision justified by the original measurements, and verify units before using the result to estimate physical material.
What you can work out here
Identify the decision first, then open the calculator that answers it.
- Triangle Calculator
- Find a triangle’s area and perimeter from three sides using Heron’s formula. All sides must use the same length unit and satisfy the strict triangle inequality.
- Rectangle Calculator
- Calculate area, perimeter and diagonal from two perpendicular side lengths. These equations require a rectangle, not an arbitrary quadrilateral.
- Circle Calculator
- Calculate radius, diameter, area and circumference from one known circle measurement. The selected measurement determines whether the input is a length or an area.
- Verify the convention
- Check the units, scope and limits before comparing results.
Core terms in plain language
Understand the recurring inputs and results instead of reading only the final number.
- Perimeter
- The sum of boundary lengths, reported in length units.
- Area
- A two-dimensional measure reported in squared length units.
- Semi-perimeter
- Half the sum of the three sides used in Heron’s formula.
- Triangle inequality
- The shorter two sides must sum to more than the longest side.
Choose with context
Which calculator should you use?
Use these distinctions to move through the Plane geometry tools without comparing unrelated results.
- 01
For a triangle, enter three valid sides; for a rectangle, enter length and width.
- 02
For a circle, choose the known radius, diameter, circumference or area before entering its value.
- 03
Keep all lengths in one unit and report area in squared units; a scaled drawing is not a site measurement.
Check the stated input format, calculation convention and limits before using the result.
Common questions
What else to know about Plane geometry
These answers explain how to use the estimates and where their limits begin.
How do I choose a tool?
For a triangle, enter three valid sides; for a rectangle, enter length and width. For a circle, choose the known radius, diameter, circumference or area before entering its value. Keep all lengths in one unit and report area in squared units; a scaled drawing is not a site measurement.
Can every set of positive sides form a triangle?
No. The shorter two sides must sum to more than the longest side. Equal sums form a degenerate line; the triangle tool rejects that input before applying Heron’s formula.