Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

# Mathematics

## Mathematical rules and laws - numbers, areas, volumes, exponents, trigonometric functions and more.

### Addition and Subtraction of Fractions

How to add and subtract fraction numbers.

### Algebraic Expressions

Principal algebraic expressions formulas.

### Angle Calculator - Carpenter's Square

Calculate angles with a straight board across carpenter's square.

### Angle Converter

Converting between angle units.

### Area of Intersecting Circles

Calculate area of intersecting circles

### Area Survey App

Online app that can be used to make an exact plot of a surveyed area - like a room, a property or any 2D shape.

### ASCII Codes

ASCII codes and characters.

### Binary Adding, Subtraction, Multiplicaton and Division

Adding, subtracting, multiplying and dividing binary numbers.

### Binary to Decimal, Hexadecimal and ASCII Converter

Convert between binary, decimal and hexadecimal numbers.

### Binary, Octal and Hexadecimal Numbers

Decimal, binary, octal and hexadecimal numbers.

### Binomial Theorem

Binomial theorem for positive integers.

### Boolean Algebra

Logic functions where the values of variables are true (1) or false (0).

### Cartesian Coordinate System - Distance and Intermediate Position Between Two Points

Distance and intermediate position between two point in a cartesian x and y coordinate system.

### Center of Gravity

A body and the center of gravity.

### Centroids of Plane Areas

The controid of square, rectangle, circle, semi-circle and right-angled triangle.

### Circle - the Chord Lengths when Divided in to Equal Segments

Calculate chord lengths when dividing the circumference of a circle into an equal number of segments.

### Circle Equation

The equation for a circle

### Circles Outside a Circle

Calculate the numbers of circles on the outside of an inner circle - like the geometry of rollers on a shaft.

### Circles within a Rectangle - Calculator

Calculate the maximum number of circles within a rectangle - can be used to calculate the numbers of pipes or wires in a conduit or similar.

### Complex Numbers

Complex numbers are used in alternating current theory and mechanical vector analysis.

### Content in Horizontal - or Sloped - Cylindrical Tanks or Pipes

Volume of partly filled horizontal or sloped cylindrical tanks or pipes - online calculator.

### Data Types

Signed vs. unsigned datatypes.

### Decimal System Prefixes

Prefix names used for multiples and submultiples units.

### Differential Calculus

Derivatives and differentiation expressions.

### Discrete Data Sets and their Mean, Median and Mode Values

Calculate the arithmetic mean, median and modal values from discrete data sets.

### Distance between 3D Points

Distance between two points in a three dimension x, y and z coordinate system - online calculator.

### Elementary Curves

Ellipse, circle, hyperbola, parabola, parallel, intersecting and coincident lines.

### Elementary Surfaces

Ellipsoid, sphere, hyperboloid, cone and more.

### Equal Areas - Circles vs. Squares

Radius and side lengths of equal areas, circles and squares.

### Exponents - Powers and Roots

The laws of fractional and integer exponents.

### Factorials

The product of all positive integers.

Law of fractions

### Fractions and Decimal Inches Equivalents

The inches fractional and decimal equivalents.

### Geometric Shapes - Areas

Areas, diagonals and more - of geometric figures like rectangles, triangles, trapezoids ..

### Hexagons and Squares - Diagonal Lengths

Distances between corners for hexagons and squares.

### Hyperbolic Functions

Exponential functions related to the hyperbola.

### Law of Cosines

One side of a triangle when the opposite angle and two sides are known.

### Law of Sines

Calculate the angles in a generic triangle.

### Law of Tangents

Triangles and law of tangents.

### Laws of Indices

Simplifying calculations by involving indices.

### Length of a Spiral

Calculate the length of a spiral or the length of material contained in a roll.

### Logarithms

The rules of logarithms - log10 and loge for numbers ranging 1 to 1000.

### Minutes vs. Degrees - Converting Chart

Convert from minutes to degrees.

### Numbers - Square, Cube, Square Root and Cubic Root Calculator

Calculate square, cube, square root and cubic root. Values tabulated for numbers ranging 1 to 100.

### Numbers - Squares, Cubes and Roots

Numbers - squares, cubes, square roots and cube roots.

### Numbers - Standard Form, Scientific and Engineering Notation

The difference between standard, scientific and engineering number notation.

### Oblique Triangle

Calculate oblique triangles.

### Optical Distance Law

Geometric dilution of light vs. distance.

### Percentage

Working with relative values.

### Pipes - Fractional Equivalents

Fractional vs. decimal inches.

### Polar vs. Cartesian Coordinates

Convert between Cartesian and Polar coordinates.

### Prime Numbers

Prime numbers up to 1000.

### Pythagorean Theorem

Verifying square corners.

### Radians vs. Degrees

Radian is the SI unit of angle. Convert between degrees and radians. Calculate angular velocity.

### Ratios and Proportions

The relative values between quantities - ratios and proportions.

### Regular Polygons

Areas of regular polygons - polygons with 3 to 12 sides.

### Right Angled Triangle

Right angled triangle equations.

### Scientific Calculator

Online scientific calculator.

### Smaller Circles within a Large Circle - Calculator

Calculate the number of small circles that fits into an outer larger circle - ex. how many pipes or wires fits into a larger pipe or conduit.

### Smaller Rectangles within a Larger Rectangle

The maximum number of smaller rectangles - or squares - within a larger rectangle (or square).

### Solids - Volumes and Surfaces

The volume and surface of solids like rectangular prism, cylinders, pyramids, cones and spheres - online calculator.

### Solving Equations of the First Degree with One Unknown

Equations with one unknown.

### Solving First Degree Equations with Two Unknowns

Online calculator and solbing procedure for two equations with two unknowns.

### Solving Quadratic Equation with One Unknown

How to solve a quadratic equation.

### Squaring with Diagonal Measurements

A rectangle is square if the lengths of both diagonals are equal.

### Standard Differentials and Integrals

Equations for differentials and integrals.

### Steradian

A unit of solid-angle measure in the International System of Units (SI)

### Taylor Series

Function as an infinite sum of terms.

### Triangle

Triangle analytical geometry.

### Trigonometric Functions

Sine, cosine and tangent - the natural trigonometric functions.

### Vector Addition

Online vector calculator - add vectors with different magnitude and direction - like forces, velocities and more.

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Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with older versions of the amazing SketchUp Make and the newer "up to date" SketchUp Pro . Add the Engineering ToolBox extension to your SketchUp Make/Pro from the Extension Warehouse !

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## Citation

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• The Engineering ToolBox (2009). Mathematics. [online] Available at: https://www.engineeringtoolbox.com/mathematics-t_54.html [Accessed Day Month Year].

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5.16.12

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