DigitHelm

Geometry calculators

Geometry tools here cover areas and perimeters of flat shapes, triangles, volumes and surface areas of solids, coordinate geometry and conic sections, ratios such as aspect ratio and map scale, and two practical estimators for flooring and paint. Each calculator names its formula and shows the substitution, so you can see where a number came from.

25 tools · Updated October 21, 2026

Showing 25 tools
Area CalculatorArea and perimeter8 m × 5 m rectangle40 m²
Aspect Ratio CalculatorProportion and scale1920 × 1080 pixels16:9
Circle CalculatorArea and perimeterCircle with a 7 cm radiusArea 153.938 cm²
Circle Sector CalculatorArea and perimeterSector, radius 10 cm, angle 60°Area 52.3599 cm²
Conic Section AnalyzerCoordinate geometry and conics4x² + 9y² − 8x − 36y − 68 = 0Ellipse, center (1, 2)
Coordinate Geometry CalculatorCoordinate geometry and conicsTriangle (0, 0), (6, 0), (2, 4)Area 12 square units
Distance CalculatorCoordinate geometry and conicsDistance from (1, 2) to (4, 6)d = 5
Ellipse CalculatorArea and perimeterEllipse with semi-axes 5 cm and 3 cmArea 47.1239 cm²
Flooring CalculatorHome project estimates15 × 12 ft room, 10% waste10 boxes of 20 sq ft
Frustum CalculatorSolids: volume and surface areaFrustum, radii 18 and 13 cm, 30 cm tall22,839.3786 cm³
Golden Ratio CalculatorProportion and scaleGolden ratio with long part 1,200Short part 741.6408
Heron's Formula Calculator, Triangle Area & AnglesTrianglesTriangle with sides 7, 8 and 9 cm26.832816 cm²
Map Scale CalculatorProportion and scale3.5 in on a 1:24,000 map1.3258 miles
Midpoint CalculatorCoordinate geometry and conicsMidpoint of (−4, 1) and (6, 5)(1, 3)
Paint CalculatorHome project estimates12 × 14 ft room, 8 ft walls, 2 coats2 gal + 2 qt
Perimeter CalculatorArea and perimeter24 × 16 ft rectanglePerimeter 80 ft
Platonic Solids CalculatorSolids: volume and surface areaDodecahedron with 5 cm edges957.8899 cm³
Pythagorean Theorem CalculatorTrianglesLegs 9 and 12, find the hypotenusec = 15
Quadrilateral Area CalculatorArea and perimeterTrapezoid, bases 14 and 8 ft, 4 ft tallArea 44 ft²
Regular Polygon CalculatorArea and perimeterHexagon with 4 in sidesArea 41.5692 in²
Slope CalculatorCoordinate geometry and conicsSlope through (−2, 1) and (4, 5)m = 2/3
Surface Area CalculatorSolids: volume and surface areaCylinder, radius 4 cm, height 15 cm477.5221 cm²
Torus CalculatorSolids: volume and surface areaTorus, radii 5 cm and 2 cm394.7842 cm³
Triangle SolverTrianglesTriangle with sides 5, 7 and 838.21°, 60°, 81.79°
Volume CalculatorSolids: volume and surface areaCylinder, radius 5 cm, height 10 cm785.4 cm³

Which one do I need?

I need the area of a rectangle, triangle, circle or other common shapeArea CalculatorI know some sides and angles of a triangle and need the restTriangle SolverI know two sides of a right triangle and need the thirdPythagorean Theorem CalculatorI want the volume of a box, cylinder, cone or sphereVolume CalculatorI have two points and need the distance, slope and midpointCoordinate Geometry CalculatorI want to resize an image or screen while keeping its aspect ratioAspect Ratio CalculatorI want to know how much flooring to buy for a roomFlooring CalculatorI need to know how many gallons of paint to buy for my wallsPaint Calculator

Length, area and volume scale differently

Perimeter is measured in units, area in square units and volume in cubic units, and that difference has practical consequences. Doubling the side of a square doubles its perimeter but multiplies its area by four; doubling the side of a cube multiplies its volume by eight. This is why a 16-inch pizza has nearly twice the area of a 12-inch one.

For flat shapes, the Area Calculator covers the common cases, while the Circle, Ellipse, Sector, Quadrilateral and Regular Polygon calculators go deeper on one shape each. For solids, use the Volume Calculator for capacity and the Surface Area Calculator for material that wraps the outside, such as paint, sheet metal or packaging.

Solving triangles

A triangle is fully determined by three pieces of information that include at least one side. With a right triangle, the Pythagorean theorem a² + b² = c² links the sides. For any triangle, the Triangle Solver uses the law of sines and the law of cosines to find the missing sides and angles, and flags the ambiguous case where two different triangles fit the same data.

When you know all three sides but no angles, Heron's formula gives the area directly from the semi-perimeter. It is handy for land plots and irregular shapes that can be split into triangles.

Coordinates, conics and real-world scale

Coordinate geometry turns shapes into algebra. The distance between two points comes from the Pythagorean theorem, the midpoint is the average of the coordinates, and the slope is rise over run. The Coordinate Geometry Calculator gives all three at once, and the Conic Section Analyzer identifies circles, ellipses, parabolas and hyperbolas from their equations.

Scale tools apply the same idea of proportion to real objects. The Map Scale Calculator turns a measured map distance into a ground distance, and the Aspect Ratio Calculator keeps screens and images in proportion when you resize them.

Questions people ask

Area measures a flat, two-dimensional region such as a floor or a wall. Surface area is the total area of all the faces or curved surfaces of a three-dimensional object. Both are in square units, but surface area applies only to solids.

Other maths topics