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Geometry Calculator
Areas, volumes, triangles and applied geometry, each one showing the formula it used.
Geometry is one subject but a great many separate formulas, and the useful question is almost never "what is the area" in the abstract — it is how much turf, how much paint, how much concrete, or whether the beam is deep enough. The pages below are grouped by what you are actually holding: a flat shape, a triangle, a solid, or a real object that happens to have a shape.
Areas of flat shapes
- MathematicsRectangle Area CalculatorArea, perimeter and diagonal of a rectangle or square.
- MathematicsTriangle Area CalculatorArea of any triangle from its base and perpendicular height.
- MathematicsCircle Area CalculatorArea, circumference and diameter of a circle from its radius.
- MathematicsTrapezoid Area CalculatorArea of a trapezoid from its two parallel sides and its height.
- MathematicsEllipse Area and PerimeterArea, approximate perimeter and eccentricity of an ellipse from its two semi-axes.
- MathematicsAnnulus (Ring) Area CalculatorArea of a ring from the outer and inner radius, with the wall thickness.
- MathematicsRegular Polygon CalculatorArea, perimeter, apothem, circumradius and interior angle of any regular polygon.
- MathematicsCircle Sector CalculatorArc length, sector area, chord and perimeter of a slice of a circle.
Triangles and coordinates
- MathematicsPythagorean Theorem CalculatorFind the hypotenuse of a right triangle from the two shorter sides.
- MathematicsTriangle Area from Three SidesArea, perimeter and height of a triangle when you only know the three side lengths.
- MathematicsTrigonometry CalculatorSine, cosine and tangent of an angle given in degrees, plus the angle in radians.
- MathematicsDistance Between Two PointsStraight-line distance, midpoint and direction angle between two coordinates.
- MathematicsSlope and Line Equation CalculatorSlope, y-intercept, angle and x-intercept of the line through two points.
- Construction & DIYSlope and Gradient CalculatorSlope as a percentage, an angle, a ratio and the sloping length.
Volumes of solids
- MathematicsBox Volume CalculatorVolume in cubic metres and litres, plus surface area, of a rectangular box.
- MathematicsCylinder Volume CalculatorVolume in cubic metres and litres, plus total surface area, of a cylinder.
- MathematicsSphere Volume CalculatorVolume and surface area of a sphere from its radius.
- MathematicsCone Volume CalculatorVolume and slant height of a cone from its radius and vertical height.
- MathematicsPyramid Volume CalculatorVolume, base area and slant height of a rectangular-based pyramid.
- Construction & DIYHorizontal Cylindrical Tank Volume CalculatorLitres in a horizontal round tank from the depth of liquid, plus the percentage full.
- Construction & DIYSwimming Pool Volume CalculatorPool volume in cubic metres and litres, plus the filtration turnover time.
Geometry on the job
- Construction & DIYLand Plot Area Calculator (four sides)Area of an irregular four-sided plot from its four sides and one diagonal, in square metres, hectares and acres.
- Construction & DIYRoom Wall Area CalculatorWall area, floor area, perimeter and volume of a rectangular room.
- Construction & DIYRoof Pitch CalculatorRoof angle, pitch percentage, rafter length and roof area per metre of length.
- Construction & DIYRamp Length CalculatorHorizontal run, sloping length and angle of a ramp for a given rise and gradient.
- Work & ProductivityAspect Ratio CalculatorResize an image or video while keeping its proportions, with the simplified ratio.
- Construction & DIYDrawing Scale ConverterTurn a measurement taken off a scale drawing into the real-world size.
- MechanicsSecond Moment of Area CalculatorI and W for a solid rectangular section and a solid round section.
- MathematicsVector Dot and Cross Product CalculatorDot product, cross product and its magnitude, the angle between two vectors and their lengths.
Which one do I need?
If the shape is flat and you want the surface, start with the areas. If you have three sides or an angle and need the rest, the triangle pages solve it — Heron's formula when you know all three sides, Pythagoras when there is a right angle, trigonometry otherwise. If it holds something, look under volumes; note that a tank lying on its side is a genuinely different calculation from one standing up. The last group is geometry already applied to a job, where the answer comes out in litres, tiles or metres of skirting.