Math & Statistics
Geometry & Trigonometry Calculators
Calculators for shapes, coordinates and angles. The Pythagorean Theorem Calculator finds a missing side of a right triangle, the Triangle Calculator solves a triangle from three known sides or angles, at least one of them a side, and the Heron’s Formula Calculator gives its area from the three sides alone. The Circle Calculator, the Polygon Area Calculator, the Sphere Calculator, the Cylinder Calculator and the Cone Calculator return areas, perimeters, surface areas and volumes. On the coordinate plane, the Distance Calculator, the Midpoint Calculator, the Slope Calculator and the Line Equation Calculator work from two points, and the Vector Calculator and the Angle Between Two Vectors Calculator handle direction as well as length. For trigonometry, the Trigonometric Functions Calculator evaluates sine, cosine and tangent in degrees or radians, the Unit Circle Calculator gives exact values at the standard angles, and the Inverse Trigonometric Functions Calculator returns the angle for a given ratio.
Triangles
- Pythagorean Theorem Calculatora² + b² = c² solved for whichever side you leave blank, with the triangle drawn to scale and integer triples reduced to their primitive.
- Triangle CalculatorSolve any triangle from three measurements — and when two sides and a non-included angle describe TWO triangles, this one shows both instead of picking one.
- Heron’s Formula CalculatorArea from three sides in the rearrangement that keeps its digits — with the textbook form shown beside it so you can see what the usual order costs.
- Special Right Triangles Calculator30-60-90 and 45-45-90 from any one side, in exact surd form as well as decimals — with the warning that the long leg is √3 times the short, not twice.
- Triangle Centers CalculatorCentroid, circumcentre, orthocentre and incentre from three coordinates — with the Euler line ratio that checks three of them against each other at once.
Geometry
- Circle CalculatorRadius, diameter, circumference and area from any one of them — and why a 16-inch pizza is four times an 8-inch one rather than twice.
- Slope Percentage CalculatorConvert a slope between percentage grade, degrees, a 1:n ratio and rise per run, or find the fall to set out across a known distance.
- Polygon Area CalculatorThe shoelace formula on any number of corners, kept exact — with the signed area whose sign is the winding direction, and a clear warning where a self-intersecting outline breaks it.
- Regular Polygon CalculatorArea, perimeter, apothem, circumradius and angles from whichever measurement you have — plus whether the polygon can be drawn with compass and straightedge at all.
- Quadrilateral CalculatorRectangle, square, parallelogram, rhombus, trapezoid and kite — each asking for the measurement its own formula needs, with the perpendicular-height trap refused rather than silently wrong.
- Ellipse CalculatorArea, perimeter, foci and eccentricity — with the perimeter approximation's error reported, because an ellipse perimeter has no exact elementary formula at all.
- Circular Segment CalculatorSegment area, chord, arc and sagitta from the angle, the chord or the height — with the sector shown alongside, because a segment is not a sector and the gap is large.
- Second Moment of Area CalculatorIx, Iy, polar J, section modulus and radius of gyration for common sections — with the parallel axis theorem, and why a joist on edge is nine times stiffer than the same joist flat.
Coordinate Geometry
- Slope CalculatorSlope as an exact fraction, with the vertical case reported as undefined rather than as a division by zero — and the angle, gradient percentage and both related slopes alongside it.
- Distance CalculatorThe distance between two points in the plane or in space, kept exact as a surd wherever the square root does not come out — √50 stays √50, and is also shown as 5√2.
- Midpoint CalculatorThe midpoint of a segment, plus the reverse problem nobody else solves: given one endpoint and the midpoint, where is the other endpoint?
- Line Equation CalculatorThe equation of a line in all three standard forms from two points or from a point and a slope, with the intercepts and the vertical case that has no y = mx + c form at all.
- Parallel and Perpendicular Lines CalculatorBoth lines through your point at once — and the two cases where the slopes-multiply-to-−1 rule does not apply, because 0 × undefined is not −1.
- Vector CalculatorMagnitude, unit vector, sum, both products and the projection — with parallelism decided on the cross product, so exactly parallel vectors return exactly 0° and not a millionth of a degree.
- Polar Coordinates CalculatorCartesian to polar and back, in two dimensions or three — with the angle from atan2, so a point in a left-hand quadrant is not reported 180° away from where it is.
- Parabola CalculatorVertex, focus, directrix, axis, latus rectum and roots — built around the focus-directrix definition that explains what all of those are actually for.
- Intersection of Two Lines CalculatorWhere two lines cross, in exact fractions — and which of the three outcomes you have, since a zero determinant means parallel or identical and those are different answers.
- Plane Equation CalculatorThe equation of a plane through three points, with its normal vector and the signed distance from a fourth — so you get which side, not only how far.
Special Functions
- Hyperbolic Functions CalculatorAll six hyperbolic functions and their inverses, built visibly from e^x and e^-x, with cosh squared minus sinh squared computed rather than asserted and every domain limit stated.
Angles
- Reference Angle CalculatorThe acute angle to the x-axis — never the y-axis — with the quadrant rule written out using your own numbers and the sign of each trig function beside it.
- Coterminal Angle CalculatorThe principal angle between 0° and 360°, the nearest negative one, and the family θ + 360n they all belong to — reduced by exact division, not by looping.
- Complementary and Supplementary Angles CalculatorBoth at once, plus the explement — and an honest answer when there is none, since an obtuse angle has no complement and a negative number is not one.
- Clock Angle CalculatorThe angle between the hands with the hour hand where it really is — at 3:30 that is 75°, not the 90° most people answer — and the face drawn to show which angle it is.
- Central Angle CalculatorLeave one of radius, arc and angle blank and the page solves for it — with the sector drawn, plus chord, sector area and segment area from the same angle.
- Angle Between Two Vectors CalculatorDot product, magnitudes and the angle as separate steps, in the plane or in space — with exactly parallel vectors returning 0° rather than a floating-point smudge.
Trigonometry
- Trigonometric Functions CalculatorAll six functions at once with exact surd values at the sixteen special angles — and tan 90° reported as undefined rather than as the 1.6 × 10¹⁶ a double returns.
- Inverse Trigonometric Functions CalculatorThe principal value AND the general solution, because a calculator hands you one member of an infinite family and the context decides which one your problem wants.
- Unit Circle CalculatorWhere an angle lands, with exact surd coordinates and the radian measure as a multiple of π — because the coordinates ARE the cosine and sine.
- Double and Half Angle Calculator2θ and θ/2 on one page, with all three forms of cos 2θ evaluated and the half-angle ± resolved from the quadrant of θ/2 — not of θ.
- Sum and Difference Identities CalculatorEach identity evaluated twice — through the formula and by computing the combined angle directly — so the agreement between them is evidence rather than a restatement.
- Phase Shift CalculatorAmplitude, period, phase shift and midline for y = A sin(Bx + C) + D — with the shift computed as −C/B, which is the step everyone skips.
Solid Geometry
- Sphere CalculatorVolume, surface area, hemisphere figures and the surface-to-volume ratio — the one number that explains why cells are small and why crushed ice cools faster.
- Cylinder CalculatorVolume with lateral and total surface area reported separately, because a pipe needs one and a sealed tin needs the other — plus the shape that uses the least material.
- Cone CalculatorVolume, slant height and both surface areas — with the vertical and slant heights kept strictly apart, because the two formulas want different ones and swapping them fails silently.
- Pyramid CalculatorVolume, both slant heights, the lateral edge and the surface areas — because a rectangular base has two slant heights and a single one is not enough.
- Prism CalculatorVolume and both surface areas for rectangular, triangular and trapezoidal prisms — with the triangular base solved from three measured side lengths, no perpendicular height needed.
- Torus and Ellipsoid CalculatorA torus is exact both ways from Pappus; an ellipsoid has an exact volume and no closed form at all for its surface area — and the page labels which is which.
Compare geometry & trigonometry calculators
What each calculator is best for, the main inputs it needs, what it shows, and what to keep in mind.
| Calculator | Best for | Key inputs | Shows | Keep in mind |
|---|---|---|---|---|
| Slope Percentage Calculator | Converting a slope between grade, degrees, and a ratio | A rise and run, a grade, an angle, or a 1:n ratio, and a run to set out | All four forms at once, plus the length along the slope | The run is horizontal, not along the slope; 100% is 45 degrees, not vertical |
| Hyperbolic Functions Calculator | All six hyperbolic functions and their inverses | One real value, |x| up to 700 | cosh²x − sinh²x against the 1 it must equal | The argument is twice a swept area, not an angle; the inverses are ar-, not arc- |