Geometry Calculator for Homework
Calculate area, perimeter, angles, and radius for 10 common shapes with step-by-step formulas
By Mathematics Education Team β’ Educational Calculator Specialist
Last updated: August 26, 2026
This calculator uses peer-reviewed geometric formulas and is built for students and educators. All results show the working formula so you learn, not just get answers.
What Is This Geometry Calculator?
This free geometry calculator computes area, perimeter, angles, radius, diameter, and circumference (or their polygon equivalents β circumradius and apothem) for ten common shapes. Pick a shape from the dropdown, enter its measurements, and get every relevant result at once using exact geometric formulas. Every calculation shows the working formula, so you understand the math β perfect for homework help or study prep.
How to Use This Calculator for Geometry Homework
- Select your shape from the dropdown (Circle, Triangle, Rectangle, Square, Rhombus, Parallelogram, Trapezoid, Pentagon, Hexagon, or any regular Polygon)
- Enter the measurements β the relevant input fields appear automatically for your chosen shape
- Click Calculate (or press Enter) to get instant results
- See the formula used β learn how each answer is derived
- Copy, Print, or Share your results to include in homework or study notes
Real-World Homework Examples
Circle Homework Problem
Problem: A circular garden has a radius of 7 meters. How much fencing do you need?
Calculator Input: Radius = 7
Answer: Circumference β 43.98 meters
The garden perimeter (circumference) is about 44 meters, so you'd need 44 meters of fencing.
Triangle Problem (SSS)
Problem: A triangular plot of land has sides of 5 ft, 6 ft, and 7 ft. What's its area?
Calculator Input: Sides = 5, 6, 7
Answer: Area β 14.70 square feet
Heron's formula solves this instantly β perfect for land surveying or construction.
Regular Hexagon Problem
Problem: A hexagonal tile has a side length of 4 cm. What's its area for the floor design?
Calculator Input: Side = 4 cm
Answer: Area β 41.57 square cm
Hexagonal tiles are popular in design β this tells you how much space each tile covers.
Formulas Used, By Shape
Circle: Circumference = 2Οr | Area = ΟrΒ²
Triangle (SSS): Area = β[s(s-a)(s-b)(s-c)] (Heron's formula), where s = perimeter Γ· 2; angles via the Law of Cosines
Rectangle: Area = length Γ width | Perimeter = 2(length + width)
Square: Area = sideΒ² | Perimeter = 4 Γ side
Rhombus: Area = (dβ Γ dβ) Γ· 2, using both diagonals
Parallelogram: Area = base Γ height | Perimeter = 2(base + side)
Trapezoid: Area = Β½ Γ (a + b) Γ height
Regular Polygon (n sides): Area = (n Γ sideΒ²) Γ· (4 Γ tan(Ο/n)) | Interior Angle = (n β 2) Γ 180 Γ· n
Understanding Each Shape
Circle
Enter either the radius or diameter β the calculator derives whichever one you didn't enter, plus circumference and area. The circle is the most symmetrical shape in geometry.
Triangle
Use "Three Sides" for full results (area, perimeter, all three angles) or "Base & Height" for a quick area-only calculation. Triangles are the simplest polygons.
Rectangle & Square
Straightforward area and perimeter, plus the diagonal length as a bonus figure. A square is just a rectangle with all equal sides.
Rhombus
Enter both diagonals β side length, area, and both pairs of interior angles are all derived from them. The diagonals of a rhombus always bisect each other at right angles.
Parallelogram
Base, adjacent side, and height together unlock area, perimeter, and both interior angles. Opposite sides are always parallel and equal.
Trapezoid
The two parallel sides and height give area; add both legs for perimeter too. Only one pair of opposite sides is parallel in a trapezoid.
Pentagon & Hexagon
Quick single-input presets (just the side length) for these two common regular polygons. A regular pentagon has 5 equal sides; a hexagon has 6.
Polygon (N-Sided)
Enter any number of sides (3-100) plus the side length for a fully general regular polygon calculation. Great for octagons, decagons, and other custom shapes.
Common Geometry Mistakes to Avoid (& How This Calculator Helps)
- Confusing diameter and radius: Radius is half the diameter. This calculator shows both, so you always know which is which.
- Triangle sides that can't form a real triangle: If the sum of any two sides is less than or equal to the third side, no triangle exists (triangle inequality). The calculator rejects these automatically with an error message.
- Forgetting Ο in circle formulas: Circumference = 2Οr and Area = ΟrΒ² β skip the Ο and your answer is completely wrong. This calculator includes it automatically.
- Using height larger than a side in a parallelogram: The perpendicular height can never be longer than the slanted side β that's geometrically impossible. The calculator validates and rejects this.
- Mixing units (cm, feet, inches): Always convert all measurements to the same unit before calculating. The calculator doesn't enforce this, but you must.
- Assuming irregular polygons work: Pentagon and Hexagon modules require regular polygons (all sides and angles equal). Irregular shapes with unequal sides won't give correct results.
- Forgetting angles in triangle calculations: You need all three side lengths (SSS mode) to calculate angles. Base & Height mode only gives area.
- Trapezoid perimeter without both legs: You can find area from just the parallel sides and height, but perimeter also needs both slanted leg lengths.
Why Students Choose This Calculator
- β Shows the formula for every result β Learn why the answer is correct, not just what it is
- β Covers 10 shapes in one place β No need to hunt for separate tools
- β Instant validation β Catches geometric impossibilities (bad triangle sides, etc.)
- β Mobile-friendly β Use on your phone during homework or study
- β Free forever β No login, no ads blocking content, no signup required
- β Copy & Print buttons β Save results for your homework folder
Frequently Asked Questions
Which shapes does this calculator support?
Circle, Triangle, Rectangle, Square, Rhombus, Parallelogram, Trapezoid, Pentagon (regular), Hexagon (regular), and any regular Polygon with 3 to 100 sides β pick a shape from the dropdown and the relevant inputs appear automatically.
What does "Circumradius" mean for a polygon?
Circumradius is the radius of the circle that passes through every vertex of a regular polygon β the polygon equivalent of a circle's radius. Apothem, shown alongside it, is the radius of the circle inscribed inside the polygon (touching the middle of each side).
How does the Triangle module work?
You can enter all three side lengths (SSS) to get area, perimeter, and all three angles via Heron's formula and the Law of Cosines, or enter just base and height for a quick area calculation β perimeter and angles require all three sides.
Why did I get an error saying my triangle sides are invalid?
This means the three lengths violate the triangle inequality β the sum of any two sides must be greater than the third side, or no such triangle can exist (for example, sides 1, 2, and 10 cannot form a triangle).
How is a rhombus different from a parallelogram or square?
A rhombus has four equal sides but angles that aren't necessarily 90Β°; a square is a special rhombus where all angles are exactly 90Β°; a parallelogram has two pairs of equal, parallel sides but doesn't require all four sides to be equal.
How do I calculate a rhombus's area and angles?
Enter both diagonals β since a rhombus's diagonals always bisect each other at right angles, the calculator derives the side length, area (half the product of the diagonals), and both pairs of interior angles directly from them.
Why does the Parallelogram module ask for base, side, AND height?
Base and height alone give you the area, but calculating the angles and perimeter also requires knowing the length of the adjacent (slanted) side β with all three, the calculator derives both interior angles using the height-to-side ratio.
What if I don't know both legs of my trapezoid?
Area only requires the two parallel sides and the height, so leave the leg fields blank (or 0) to get area alone β enter both leg lengths as well if you also want the perimeter.
Why are Pentagon and Hexagon separate from the general Polygon module?
They're just quick-access shortcuts for two of the most common regular polygons (5 and 6 sides) β enter only the side length. The general Polygon module handles any regular polygon from 3 to 100 sides if you need something else, like a regular octagon or decagon.
Does this calculator handle irregular polygons?
No β the Polygon, Pentagon, and Hexagon modules assume a regular polygon (all sides and angles equal). Irregular shapes with unequal sides aren't supported in this version.
How accurate are the results?
All calculations use exact geometric formulas (not approximations), so results are as accurate as the measurements you enter, rounded for display to a reasonable number of decimal places.
Is there a more detailed Triangle-only tool?
Yes β the dedicated Triangle Calculator on this site offers a more focused triangle-specific experience if that's the only shape you need.
Related Geometry Tools
If you need more focused tools for specific shapes, explore our other calculators:
Conclusion
This geometry calculator is built for students who want to understand their math, not just get answers. Whether you're solving homework problems, preparing for a test, or learning geometry concepts, the combination of instant calculations and visible formulas gives you confidence in your work.