Geometry guides
Master geometric calculations with step-by-step solutions for areas, volumes, perimeters, and more.
34 guides · each with a free step-by-step calculator
Geometry Math Solver: Complete Guide to Calculating Areas, Volumes & Perimeters
How much paint covers a wall? How much water fits in a tank? How long is the fence around a garden? These are all geometry questions. In this guide you'll learn the three big ideas behind every shape problem, perimeter, area and volume, and a simple method to solve any of them step by step.
Area Calculator: How to Calculate Area for Any Shape with Step-by-Step Solutions
Why does a triangle's area formula have a ½ in it? Because every triangle is exactly half of a rectangle. Once you see how area formulas connect like this, you stop memorising and start understanding. This guide shows you how to find the area of rectangles, triangles, circles, trapezoids and even odd-shaped rooms.
Volume Calculator: Master 3D Shape Calculations with Step-by-Step Solutions
Here is a surprising fact: an ice-cream cone holds exactly one third of the ice cream of a cylinder with the same base and height. Volume is full of neat patterns like this. In this guide you'll learn what volume means, the formulas for boxes, cylinders, cones and spheres, and how to turn cubic metres into litres.
How to Find the Area of a Circle (Easy Guide)
Is a 16-inch pizza really a better deal than two 12-inch pizzas? The answer surprises most people, and it comes down to one short formula. By the end of this guide you'll be able to find the area of any circle in under a minute.
How to Find the Area of a Rectangle
How much flooring should you actually order for a rectangular bedroom? Guess wrong and you either run short mid-job or pay for tiles you never use. This guide shows you the one multiplication that gets it right every time.
How to Find the Area of a Square
Ever wonder why a phone screen that's 6 inches diagonal costs so much more to fully protect than a 5-inch one? Squares (and near-squares) grow area fast. Here's the one measurement and one formula you need.
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How to Find the Perimeter of a Rectangle
Two yards can need the exact same length of fencing yet hold very different amounts of space inside. That's the twist with perimeter — it only cares about the edge, not what's inside it. Here's how to measure it correctly.
How to Find the Perimeter of a Square
If you have 28 meters of edging, a square plot gives you more growing space than almost any other rectangle you could make with the same edging. Here's the quick formula behind that, and how to use it.
How to Find the Volume of a Cube
Double the size of a storage box and you might expect it to hold twice as much. It actually holds eight times as much. That jump is what makes cube volume worth understanding before you buy a box, a tank, or a mold.
How to Find the Area of a Triangle
A tall, skinny triangle and a short, wide one can cover the exact same amount of fabric — as long as the base and height match. This guide shows you the one formula that works for every triangle, no matter its shape.
How to Find the Circumference of a Circle
Every time a bike wheel spins once, it travels exactly as far as its own circumference — that's literally how bike computers calculate your speed. This guide shows you how to find that distance for any circle.
How to Find the Volume of a Rectangular Prism
Two boxes with wildly different shapes can hold the exact same amount, which is exactly why "cubic capacity" and "will it fit through the door" are two separate questions. This guide covers the first one.
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Pythagorean Theorem Explained (With Examples)
Builders check that a corner is truly square using nothing but a tape measure and one ancient formula. It works for ladders against walls, TV diagonals, and city blocks too. Here's how it works and how to use it.
How to Use the Distance Formula (With Steps)
Video games, maps, and navigation apps all rely on one question: how far apart are two points, in a straight line? The distance formula answers it using nothing more than the Pythagorean theorem in disguise.
How to Find the Midpoint Between Two Points
Two friends who live across town from each other want a genuinely fair meeting spot, not one that's just eyeballed. The midpoint formula finds that exact halfway point using nothing but simple averages.
How to Find the Surface Area of a Sphere
Coating a spherical tank in protective paint costs a lot more than you'd guess from its size — because a sphere's outer skin grows with the square of the radius, not the radius itself. Here's exactly how much material you'll need.
How to Find the Volume of a Sphere
A basketball only a little bigger than a tennis ball actually holds many times more air. That's because a sphere's volume grows with the radius cubed. Here's the formula behind that jump, and how to use it.
How to Find the Area of a Parallelogram
Push the top of a rectangle sideways into a slanted shape, and something surprising happens: the area doesn't change at all, as long as the base and height stay the same. Here's the formula behind that trick.
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How to Find the Area of a Trapezoid
A table with a wider top than bottom, a lampshade panel, an oddly shaped garden plot — trapezoids are everywhere once you start looking. This guide shows you how one simple average handles them all.
How to Find the Volume of a Cylinder
A soda can, a water tank, a drinking glass — all cylinders, and all figured out the same way. Find the area of the circular end, then stretch it up by the height. That's the whole idea behind this formula.
How to Find the Surface Area of a Cylinder
Peel the paper label off a soup can and lay it flat, and you get a plain rectangle. Add back the two circular ends, and you've just built a cylinder's entire surface area formula by hand.
How to Find the Volume of a Cone
Fill a cone-shaped cup with water and pour it into a same-sized cylinder, and you'll need to do it three times before the cylinder is full. That 1-in-3 relationship is the whole secret behind this formula.
How to Find the Surface Area of a Cone
Party hats and traffic cones both need a hidden extra step before you can find their surface area: measuring the slant, not the straight-up height. Here's why, and how to do it correctly.
Heron's Formula: Triangle Area From 3 Sides
Surveyors measuring an oddly shaped triangular plot of land almost never have a way to plant a perpendicular height. Heron's formula solves that problem completely, using only the three boundary lengths.
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How to Find the Area of a Rhombus
A kite in the sky is really just a rhombus, and its two crossing sticks are the exact measurements you need to find its area. No base, no height — just the two diagonals.
How to Find the Area of a Sector (Pie Slice)
One slice from a large pizza and one slice from a small pizza can be cut at the exact same angle and still be worlds apart in size. The trick is that a sector's area depends on both the angle and the radius. Here's how.
How to Find the Arc Length of a Circle
Runners on the curved part of a track cover more ground per lap the further out they are, even sharing the exact same angle of turn. That's arc length at work, and this guide breaks down exactly how to calculate it.
How to Find the Volume of a Pyramid
A pyramid-shaped tent looks like it should hold nearly as much as a box with the same footprint and height. It actually holds exactly one-third. This guide shows why, and how to calculate it for yourself.
How to Find the Area of an Ellipse
Stretch a circle in one direction and you get an oval — an ellipse. Its area formula is nearly identical to a circle's, just using two radius-like measurements instead of one. Here's how it works.
How to Find the Surface Area of a Cube
Wrap a gift box in paper and you're really solving a surface area problem: six identical square faces, all needing coverage. This guide shows the one small formula that gets the total right every time.
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How to Find the Sum of Interior Angles
A stop sign is a perfect regular octagon, and every single one of its eight corners bends at exactly 135°, guaranteed by nothing more than counting the sides. This guide shows you the formula behind that guarantee.
How to Find the Diagonal of a Rectangle
TV and monitor sizes are always advertised as a single diagonal measurement, corner to corner, never the width or height alone. This guide shows how that one number connects to the two sides using an old, reliable theorem.
How to Find the Perimeter of a Triangle
Before you buy fencing for a triangular garden, there's one rule worth knowing: not just any three lengths will actually form a triangle. This guide covers both the simple formula and the check that keeps it valid.
How to Calculate BMI (Body Mass Index)
What does that one number on a health chart, 'BMI,' actually measure? It's just weight divided by height squared, a simple screening calculation, not a diagnosis, and this guide walks through exactly how it's worked out.
