Mapping Scales

Overview

Engineering reference data for Mapping Scales in mathematics.

Key Formulas

Quadratic Formula

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Roots of ax² + bx + c = 0.

Pythagorean Theorem

$c^2 = a^2 + b^2$

Right triangle relationship.

Circle Area

$A = \pi r^2$

Area of a circle.

Logarithm

$\log_b(x) = \frac{\ln(x)}{\ln(b)}$

Change of base formula.

Variables

Symbol	Description	Unit
$\pi$	Pi	3.14159...
$e$	Euler's number	2.71828...

Examples

Example: Scale 1:100

The scale of a drawing is 1:100. From the table, the conversion factor is $1.0 \text{ m/cm}$. $1 \text{ cm (drawing)} \times 1.0 \text{ m/cm} = 1 \text{ m (real)}$

Example: Scale 1:10000

The scale of a map is 1:10000. From the table, the conversion factor is $0.1 \text{ km/cm}$. $1 \text{ cm (map)} \times 0.1 \text{ km/cm} = 0.1 \text{ km (real)}$

Example: Converting a Rate

A rate of $0.1 \text{ miles/inch}$ corresponds to:

• A scale of approximately *1:6300
• A conversion factor of approximately 63 m/cm

Interactive Charts

References

• Original Source