Geometry Formulas
Shape & Volume Calculations
Essential geometric formulas for area, volume, perimeter, and surface area calculations
🔢Important Geometric Constants
2D Shapes - Area & Perimeter
Rectangle Area
Length × width
Rectangle Perimeter
Two times (length + width)
Square Area
Side squared
Square Perimeter
Four times side length
Triangle Area
Half base times height
Triangle Perimeter
Sum of all three sides
Circle Area
Pi times radius squared
Circle Circumference
Two pi times radius
Triangles - Special Cases
Right Triangle (Pythagorean)
Sum of squares of legs equals hypotenuse squared
Equilateral Triangle Area
Special formula for equal-sided triangle
Triangle Area (Heron's)
Using semi-perimeter s = (a+b+c)/2
30-60-90 Triangle
Special right triangle ratios
45-45-90 Triangle
Isosceles right triangle ratios
Triangle Height
Height from area and base
3D Shapes - Volume
Cube Volume
Side cubed
Rectangular Prism
Length × width × height
Cylinder Volume
Pi × radius² × height
Sphere Volume
Four-thirds pi radius cubed
Cone Volume
One-third pi radius² height
Pyramid Volume
One-third base area times height
Triangular Prism
Half × base × width × height
Ellipsoid Volume
Four-thirds pi times three radii
3D Shapes - Surface Area
Cube Surface Area
Six times side squared
Rectangular Prism SA
Two times sum of face areas
Cylinder Surface Area
Two circular bases plus lateral area
Sphere Surface Area
Four pi radius squared
Cone Surface Area
Base area plus lateral area (l = slant height)
Pyramid Surface Area
Base area plus half perimeter times slant height
Coordinate Geometry
Distance Formula
Distance between two points
Midpoint Formula
Point halfway between two points
Slope Formula
Rise over run
Point-Slope Form
Line equation using point and slope
Slope-Intercept Form
Line equation with slope and y-intercept
Circle Equation
Circle with center (h,k) and radius r
Advanced Geometry
Trapezoid Area
Half times sum of parallel sides times height
Parallelogram Area
Base times height
Rhombus Area
Half the product of diagonals
Regular Polygon Area
Half perimeter times apothem
Sector Area
Fraction of circle based on central angle
Arc Length
Fraction of circumference based on angle
Ellipse Area
Pi times semi-major times semi-minor axis
Torus Volume
Donut shape: major radius R, minor radius r
Common Unit Conversions
Length
Area
Volume
🔺Special Triangle Quick Reference
30-60-90 Triangle
45-45-90 Triangle
Right Triangle
About Geometry
Geometry is the branch of mathematics concerned with the properties and relationships of points, lines, surfaces, and solids. It encompasses both plane geometry (2D shapes) and solid geometry (3D objects), providing the foundation for understanding spatial relationships and measurements in our physical world.
These geometric formulas are essential tools for calculating areas, volumes, perimeters, and surface areas of various shapes and objects. From basic rectangles and circles to complex 3D solids, these formulas enable precise measurements and calculations needed in fields ranging from architecture and engineering to art and design.
Whether you're a student learning fundamental geometric concepts, an architect designing buildings, or an engineer calculating material requirements, these formulas provide the mathematical foundation for accurate spatial calculations and problem-solving.
How to Apply Geometric Formulas
Identify the Shape
Determine what geometric shape you're working with and what measurement you need to find.
Gather Known Measurements
Collect all given measurements (length, width, radius, height, etc.) and ensure they're in the same units.
Select the Correct Formula
Choose the appropriate formula that relates the known measurements to what you need to find.
Calculate and Verify
Substitute values into the formula, calculate the result, and check that it makes geometric sense.
Geometry Study Tips
Draw Diagrams
Always sketch the shape and label known measurements to visualize the problem.
Check Units
Ensure all measurements are in the same units before calculating.
Practice Variations
Work with different shapes and learn to rearrange formulas to solve for different variables.
Memorize Key Formulas
Focus on memorizing the most commonly used formulas for basic shapes.
Understand Relationships
Learn how formulas relate to each other and can be derived from basic principles.
Verify Reasonableness
Check that your answers make sense in the context of the problem.
Frequently Asked Questions
Get answers to common questions about geometry formulas