Geometry Calculators gather twenty-six tools for triangles, two-dimensional figures, three-dimensional solids and coordinate geometry. Each page draws a labelled figure to the numbers entered, solves for missing measures, and shows the substituted arithmetic beside the result so a hand check is possible.
The hub groups pages by topic. Triangle tools handle general solving, right-angle shortcuts and the Pythagorean theorem. Plane-shape pages report area and perimeter in the length unit squared. Solid pages label lateral and total surface area separately where both apply, and volume in cubic units. Slope, distance and midpoint share a two-point engine while each page owns its primary output.
Triangles
The Triangle Calculator accepts any three of six measurements and reports the detected case, including both valid triangles in the ambiguous SSA situation when they exist. The Right Triangle Calculator fixes the 90 degree angle and finishes the shape from two sides or one side and an acute angle.
The Pythagorean Theorem Calculator applies a squared plus b squared equals c squared, tests the converse on three sides, and lists common integer triples.
| Tool | Primary output |
|---|---|
| Triangle Calculator | All sides, angles, area, case name |
| Right Triangle Calculator | Legs, hypotenuse, trig ratios, area |
| Pythagorean Theorem Calculator | Hypotenuse, leg, converse test |
Open the page that matches the angle or side information available. Neighbouring triangle pages cross-link without repeating the same worked example.
Two-dimensional shapes
Circle, rectangle with square mode, parallelogram, rhombus, trapezoid, regular polygon, annulus and stadium pages each own one figure family. Area uses square units for the chosen length unit. Circumference and perimeter stay in linear units. The circle page also reports arc length and sector area from a central angle.
| Tool | Primary output |
|---|---|
| Circle Calculator | Radius, diameter, area, circumference, arc |
| Rectangle Calculator | Area, perimeter, diagonal, square mode |
| Parallelogram Calculator | Area from base and height |
| Rhombus Calculator | Area from diagonals, side length |
| Trapezoid Calculator | Area, median, parallel bases |
| Polygon Calculator | Interior angle, area, apothem for regular n-gons |
| Annulus Calculator | Ring area between two radii |
| Stadium Calculator | Discorectangle area and perimeter |
Dedicated solid pages link to related two-dimensional partners where useful, such as circle to sphere or stadium to capsule, without duplicating full three-dimensional treatments.
Solids and surface area
Cone, cylinder, sphere, hemisphere, pyramid, rectangular prism, triangular prism, capsule, tube, conical frustum and pyramid frustum pages each report volume and the surface areas that apply. The multi-shape Surface Area Calculator selects among common solids when the question is surface area of a named shape rather than every measure of one solid.
| Tool | Primary output |
|---|---|
| Cone Calculator | Volume, slant height, lateral and total SA |
| Cylinder Calculator | Volume, lateral and total SA |
| Sphere Calculator | Volume and surface area |
| Hemisphere Calculator | Volume and total SA including base |
| Pyramid Calculator | Square-base volume and slant height |
| Rectangular Prism Calculator | Volume, surface area, space diagonal |
| Triangular Prism Calculator | Volume from triangle base times length |
| Capsule Calculator | Pill-shaped volume and surface area |
| Tube Calculator | Hollow cylinder material volume |
| Conical Frustum Calculator | Truncated cone volume |
| Pyramid Frustum Calculator | Truncated square pyramid volume |
| Surface Area Calculator | SA for selected solid type |
Lateral area names the curved or side faces only. Total surface area includes bases where the solid has them.
Coordinate geometry
Slope, distance and midpoint pages accept two points in the plane. Distance applies the Pythagorean theorem on horizontal and vertical separations. Slope reports rise over run, the inclination angle in degrees, and the slope-intercept line equation when defined. Midpoint averages coordinates and can recover a missing endpoint when one end and the center are known.
| Tool | Primary output |
|---|---|
| Slope Calculator | Gradient, angle, line equation |
| Distance Calculator | Straight-line distance, 3D option |
| Midpoint Calculator | Center point, endpoint recovery |
The Pythagorean Theorem Calculator explains why the distance formula matches the theorem on a grid.
How the numbers are produced
Formula constants and reference fixtures load from the shared geometry reference file so worked examples on hub pages match the arithmetic shown on individual calculators. Engines are pure functions. Pages show substituted steps where the UI supports a breakdown list.
Results use the same unit system as the inputs. Angles accept degrees or radians where relevant. Invalid combinations, such as a hypotenuse shorter than a leg, return a clear message instead of a silent guess.
Frequently asked questions
Do all geometry pages show the working?
Yes. Shape A pages include substituted arithmetic for every formula on the page, aligned with the geometry reference fixtures where a standard example exists.
Which page solves a general triangle?
The Triangle Calculator. Right Triangle Calculator and Pythagorean Theorem Calculator cover the 90 degree cases with fewer inputs.
Where is surface area for several shapes in one place?
The Surface Area Calculator selects a solid type. Dedicated solid pages still own the full volume and slant-height treatment for that shape.
How do stadium and capsule relate?
A stadium is the two-dimensional running-track outline. A capsule is the three-dimensional pill shape built from a cylinder and two hemispherical ends.
Which page finds the slope of a line through two points?
The Slope Calculator. It also reports the angle of inclination and the equation y equals m x plus b when the line is not vertical.
Summary
This hub lists geometry calculators for triangles, plane figures, solids and coordinate work. Each tool draws a labelled figure, supports solve-for-any-variable where the shape allows it, and shows substituted working. Pick the page named for the quantity being solved and read the related links for neighbouring questions.