Plane Geometry Calculator
Calculate area, perimeter, and key properties for 10 common 2D shapes. Select a shape, enter your known values, and get instant results.
Shape Formulas at a Glance
Shape formulas for area and perimeter are the foundation of plane geometry. Use this quick reference for the 10 most common shapes.
C = 2πr
P = 2(l+w)
P = 4s
P = a+b+c
P = a+b+c+d
P = 2(a+b)
P = 4a
P = 2π(R+r)
P ≈ π(3(a+b)−√…)
P = n × s
Area and Perimeter Reference Table
Area and perimeter formulas for common shapes in one printable table. All formulas use standard variable notation.
| Shape | Area Formula | Perimeter Formula | Key Variables |
|---|---|---|---|
| Circle | A = π r² | C = 2πr | r = radius |
| Rectangle | A = l × w | P = 2(l + w) | l = length, w = width |
| Square | A = s² | P = 4s | s = side length |
| Triangle (base/height) | A = ½ b h | P = a + b + c | b = base, h = height |
| Trapezoid | A = ½(a + b)h | P = a + b + c + d | a, b = parallel sides |
| Parallelogram | A = b × h | P = 2(a + b) | b = base, h = height |
| Rhombus | A = (d1 × d2) / 2 | P = 4a | d1, d2 = diagonals |
| Annulus | A = π(R² − r²) | P = 2π(R + r) | R = outer r, r = inner r |
| Ellipse | A = π a b | P ≈ π(3(a+b)−√((3a+b)(a+3b))) | a = semi-major, b = semi-minor |
| Regular Polygon | A = ns²/(4tan(π/n)) | P = n × s | n = sides, s = side length |
What Is Plane Geometry?
Plane geometry is the study of flat, two-dimensional shapes and their properties. It covers measurements like area and perimeter, angle relationships, symmetry, and the spatial relationships between points, lines, and curves. All shapes in plane geometry exist on a single flat surface with no depth.
Area vs. Perimeter
Area measures the space enclosed inside a 2D shape, expressed in square units such as cm² or m². Perimeter measures the total length of the boundary around a shape, expressed in linear units such as cm or m. For a circle, the boundary is called the circumference rather than the perimeter.
Why Units Matter
Always keep all inputs in the same unit. If you enter side lengths in centimetres, your area result will be in cm² and your perimeter in cm. Mixing units (for example, base in metres and height in centimetres) produces incorrect results.
Common Plane Geometry Shapes Explained
Circle
A circle is defined by all points equidistant from a centre point. The radius r is the distance from the centre to the edge. The diameter d = 2r. Area = πr² and circumference C = 2πr.
Triangle
A triangle has three sides and three interior angles that always sum to 180°. Area = (1/2) × base × height. For a triangle where all three side lengths are known, Heron’s formula gives the area without needing the height: A = √(s(s−a)(s−b)(s−c)) where s is the semi-perimeter.
Trapezoid
A trapezoid (or trapezium) has exactly one pair of parallel sides, called the bases. Its area is (1/2) × (base1 + base2) × height. The perimeter sums all four sides.
Annulus
An annulus is the ring-shaped region between two concentric circles. Its area equals the area of the outer circle minus the area of the inner circle: A = π(R² − r²). This shape appears in pipe cross-sections, washers, and circular tracks.
Frequently Asked Questions
Answers to the most common plane geometry questions, written for fast understanding.