2D Shape Calculators

2D Shape Calculators - Area, Perimeter, and Dimensions for Every Flat Shape

Two-dimensional shape calculations appear in construction (floor area, tile count), landscaping, design, education, and everyday problem-solving. These calculators support multiple input combinations so you can work with whatever measurements you have available.

Thirty-Seven 2D Shape Calculators

Area Calculator - Multi-shape area and perimeter calculator covering eight 2D shapes in one tool: rectangle, triangle, circle, trapezoid, parallelogram, ellipse, sector, and regular polygon. Each mode shows area in square units and the matching perimeter or circumference. Use when you need to compare areas across different shape types.

Area of a Circle Calculator - Focused calculator for circle area: A = pi times r squared. Three input modes: enter radius, diameter, or circumference and get area, circumference, diameter, and radius instantly. Dedicated to the single most-searched circle question, with worked examples from r = 7 to the Earth’s radius.

Area of a Right Triangle Calculator - Calculate right triangle area from three input combinations: two legs (A = 0.5 times a times b), hypotenuse plus one leg (uses Pythagorean theorem to find the missing leg), or hypotenuse plus angle (uses sin and cos to derive both legs). Also outputs the hypotenuse, missing leg, and perimeter. Covers all Pythagorean triples and special right triangles including 30-60-90 and 45-45-90.

Centroid Calculator

Circumscribed Circle Calculator - Find the circumscribed circle (circumcircle) for any triangle or regular polygon. Triangle by Sides mode uses R = abc / (4K) with Heron’s formula. Triangle by Angle mode applies the Law of Sines: R = a / (2 sin A). Regular Polygon mode uses R = s / (2 sin(pi/n)) for any polygon from triangle (n=3) to dodecagon (n=12). Outputs circumradius, circumcircle area, circumference, and triangle or polygon area.

Circle Theorems Calculator - Apply the four major circle theorems: Central & Inscribed Angle (inscribed angle = central angle ÷ 2), Chord-Chord Angle (angle = (arc1 + arc2) ÷ 2), Tangent-Chord Angle (angle = arc ÷ 2), and Secant-Secant External Angle (angle = (far arc − near arc) ÷ 2). Enter arc or angle values to get the unknown angle with the theorem formula shown.

Circumference Calculator - Calculate the circumference (perimeter) of a circle from radius (C = 2 pi r), diameter (C = pi d), or area. All four circle properties are shown. Covers the unit circle, tire circumference, circular fence length, and the Earth’s circumference. Pairs naturally with the Area of a Circle Calculator.

Circle Calculator - Enter any one known value (radius, diameter, circumference, or area) and get all others instantly. Area = πr², Circumference = 2πr. Also shows sector area and arc length for a given central angle. Used for circular garden beds, cylindrical cross-sections (pair with the Cylinder Calculator), wheels, and pipes.

Cross-Sectional Area Calculator - Calculate cross-sectional area for four engineering section shapes: solid circle (A = pi r squared), hollow circle or pipe (A = pi times R squared minus r squared), rectangle (A = b times h), and I-beam (A = 2 times bf times tf plus hw times tw). Also outputs circumference, wall thickness, perimeter, or web height depending on the selected shape. Used in structural engineering, mechanical design, and pipe flow calculations.

Ellipse Calculator - Enter semi-major axis a and semi-minor axis b to get area (πab), perimeter (Ramanujan’s formula, accurate to 0.0001%), eccentricity, focal distance c, foci coordinates, and semi-latus rectum. Covers planetary orbits, oval tracks, elliptical pools, and optical reflectors. A circle is the special case where a = b.

Equation of a Circle Calculator - Find the equation of a circle in both standard form (x minus h) squared plus (y minus k) squared equals r squared and expanded general form. Three modes: Center and Radius (enter h, k, r directly), Three Points (finds the unique circle through any three non-collinear coordinate pairs using a 2x2 linear system), and General Form (converts x squared plus y squared plus Dx plus Ey plus F = 0 back to center and radius by completing the square). Also outputs area and circumference.

Rectangle Calculator - Enter length and width to get area, perimeter, and diagonal (using the Pythagorean theorem: d = √(l² + w²)). Or enter area and one side to find the other. Used for room area, plot sizes, screen dimensions, and material cutting plans.

Square Calculator - Enter side length to get area (s²), perimeter (4s), and diagonal (s√2). Works in reverse: enter area to find side length. Used for square tiles, floor sections, and square land parcels.

Square in a Circle Calculator - Two-mode calculator: Inscribed Square (enter circle radius, find the largest square that fits inside using side = r times sqrt(2)) and Circumscribed Circle (enter square side, find the enclosing circle using r = s times sqrt(2) / 2). Shows square area, perimeter, diagonal, circle area, circumference, and the constant area ratio (square fills 63.66% of circle). Used for square-peg-in-round-hole problems, log-to-timber milling, and circular courtyard design.

Triangle Calculator - Three input methods: (1) base and height → Area = ½ × base × height, (2) all three sides → Heron’s formula, (3) two sides and included angle → Area = ½ab·sin(C). Also computes perimeter and identifies triangle type. For angle-based work, combine with the Sin Cos Tan Calculator.

Trapezoid Calculator - Area = ½ × (a + b) × h where a and b are the parallel sides. Three modes: general, isosceles, and right trapezoid. Also computes perimeter, midsegment, and diagonals. Used in civil engineering cross-sections, retaining wall profiles, and surveying irregular land parcels.

Parallelogram Calculator - Two input modes: (1) base and perpendicular height → Area = b × h, (2) base, side, and included angle → Area = a × b × sin(θ). Returns area, perimeter, both diagonals, and perpendicular height. Covers the general case and all special forms - rectangles (θ = 90°), rhombuses (a = b), and squares. Applied in structural engineering (inclined cross-sections), physics (parallelogram of forces), and design.

Pythagorean Theorem Calculator - Three modes: (1) find the hypotenuse from two legs using c = √(a² + b²), (2) find a missing leg from the hypotenuse and one leg, (3) verify if three numbers form a Pythagorean triple. Shows area and perimeter of the resulting right triangle. Also covers common Pythagorean triples (3-4-5, 5-12-13, 8-15-17).

Pythagorean Triples Calculator - Three modes: Generate lists all primitive and non-primitive Pythagorean triples up to any hypotenuse limit (up to 5000), labeled and sorted by hypotenuse. Check verifies whether three integers satisfy a squared plus b squared equals c squared with full arithmetic shown. Euclid’s Formula generates the triple for any (m, n) pair using a = m squared minus n squared, b = 2mn, c = m squared plus n squared.

Right Triangle Calculator - Fully solve any right triangle from any two known values. Three modes: two legs, hypotenuse + one leg, or one acute angle + one side. Returns all three sides, both acute angles (degrees), area, and perimeter. Uses the Pythagorean theorem and SOH CAH TOA trig ratios automatically.

Right Triangle Side and Angle Calculator - Four input modes (two legs, leg + hypotenuse, angle + hypotenuse, angle + leg) with all six trig ratios (sin, cos, tan, csc, sec, cot) for both acute angles. Also shows area, perimeter, and altitude to the hypotenuse. Full SOH-CAH-TOA solver with step-by-step trig values.

30-60-90 Triangle Calculator - The 30-60-90 special right triangle has sides in the ratio 1 : √3 : 2. Enter any one side (short leg, long leg, or hypotenuse) to instantly find all three sides, area, and perimeter. Three input modes, full formula shown. Essential for geometry, trigonometry, and construction work where these angles appear frequently.

Equilateral Triangle Calculator - All three sides equal, all angles 60°. Three input modes: enter side length, height, or area. Returns all three sides, height (h = s√3/2), area (A = s²√3/4), perimeter, inradius, and circumradius. Used for truss design, tiling, and any symmetric triangular structure.

Sector Area Calculator - A sector is the “pie slice” region bounded by two radii and an arc. Enter radius and central angle (in degrees or radians) to find sector area, arc length, chord length, and sector perimeter. Area = ½r²θ (radians) = (θ/360)πr² (degrees). Used for pie charts, sprinkler coverage, gear design, and circular segment problems.

Isosceles Triangle Calculator - Two sides equal (the “legs”), base potentially different. Two input modes: (1) legs + base, (2) legs + apex angle. Returns base, legs, height, apex angle, base angles, area, and perimeter. Validates the triangle inequality automatically. Applied in architecture (gable roof shapes), bridges, and symmetric truss design.

45-45-90 Triangle Calculator - The isosceles right triangle with sides in ratio 1 : 1 : √2. Enter one leg or the hypotenuse to find all sides, area, and perimeter instantly. Two input modes. Used in design (diagonal cuts at 45°), construction, and any symmetric right-angle problem where the two legs are equal.

Special Right Triangles Calculator - Combined calculator for both special right triangles in one place. 45-45-90 mode (isosceles right triangle, ratio 1:1:root2) and 30-60-90 mode (half equilateral triangle, ratio 1:root3:2). Enter any one known side to find all sides, area, and perimeter instantly for either triangle type.

Semicircle Area Calculator - Find area, arc length, and perimeter of a semicircle from radius, diameter, or area. Three input modes. Area = πr²/2; Perimeter = r(π+2). Used for arch design, D-shaped land parcels, semicircular windows, and half-round pool covers.

Segment Area Calculator - A circular segment is the region between a chord and the arc it subtends. Enter radius and central angle (degrees or radians) to find segment area, chord length, arc length, and sagitta (height). Area = r²(θ − sin θ)/2. Used in hydraulics (partially-filled pipes), lens design, and cam profiles.

Triangle Height Calculator - Find the height (altitude) of any triangle. Three modes: (1) base + area → height, (2) all three sides → all three altitudes via Heron’s formula, (3) right triangle leg + hypotenuse → altitude to hypotenuse. Used whenever a triangle’s dimensions are known except the perpendicular height.

Triangle Area Calculator - Three methods: (1) base × height (÷2), (2) Heron’s formula for all three sides, (3) two sides and included angle (SAS). Returns area and - where possible - perimeter and triangle type. The most versatile triangle area tool for any combination of known measurements.

Triangle Angle Calculator - Find all angles of a triangle. Two modes: (1) SSS - enter all three sides, angles computed via the Law of Cosines (cos A = (b²+c²−a²)/2bc); (2) Two Angles - enter two angles and the third is found using A+B+C = 180°. Classifies the triangle as acute, right, or obtuse and verifies the triangle inequality.

Triangle Inequality Theorem Calculator - Enter three side lengths to verify all three triangle inequality conditions (a + b greater than c, a + c greater than b, b + c greater than a) with pass or fail indicators and actual arithmetic. For valid triangles, also shows area (Heron’s formula), perimeter, all three angles (Law of Cosines), and triangle type by sides (equilateral, isosceles, scalene) and by angles (acute, right, obtuse).

Perimeter of a Triangle Calculator - Two modes: (1) SSS - add all three sides directly; (2) SAS - enter two sides and the included angle, compute the third side using the Law of Cosines, then sum. Also shows area via Heron’s formula and all three angles. Works for any triangle type.

Similar Triangles Calculator - Enter all three sides of Triangle 1 and one corresponding side of Triangle 2. The calculator finds the scale factor k, all missing sides of Triangle 2, the area ratio (k²), and the perimeter ratio (k). Useful for map scaling, architectural drawings, and shadow-length problems.

Classifying Triangles Calculator - Enter three side lengths to classify a triangle by sides (equilateral, isosceles, scalene) and by angles (acute, right, obtuse). Also shows all three angles via the Law of Cosines, area via Heron’s formula, perimeter, and the triangle inequality verification.

Tangent of a Circle Calculator - Two-mode calculator for circle tangents. Tangent Length mode: enter circle radius and distance from an external point to the center to find tangent length (L = sqrt(d squared minus r squared)), the angle between both tangents at the external point, the central angle at the circle, and the quadrilateral area. Tangent Line Equation mode: enter center coordinates, radius, and slope to get both parallel tangent line equations and their y-intercepts. Uses the equal tangent theorem and Pythagorean triples for verification.

Real-World Applications

Flooring - Use the Rectangle Calculator for room area, divide by tile size, add 10% for cuts and wastage. For diamond-pattern or angled tiles, use the Parallelogram Calculator to compute each tile’s true area. Circular structures - The Circle Calculator handles round garden beds, pools, and cross-sections. Oval shapes - The Ellipse Calculator covers oval tracks, elliptical ponds, and any shape with two unequal axes. Land measurement - Area outputs are available in square metres, square feet, and square yards for Indian plot conventions. Irregular plots with one pair of parallel sides are trapezoids - use the Trapezoid Calculator.