Order of Magnitude Calculator
Convert numbers to scientific notation and find their order of magnitude
Calculate Order of Magnitude
Supports standard notation, decimals, and scientific notation (e.g., 1.5e-10)
Order of Magnitude Result
Example Calculations
Very Small - Atomic Scale
Mass of a helium atom (kg)
Small - Microscopic
1 micrometer in meters
Human Scale
Average human height (meters)
Large - Planetary
Mass of Earth (kg)
Very Large - Astronomical
Mass of the Sun (kg)
Simple Example
Order of magnitude is 3
Quick Reference
Scientific Notation
a = b x 10ⁿ where 1 ≤ |b| < 10
Order of Magnitude
The exponent n in scientific notation
Formula
n = floor(log₁₀(|a|))
Common Scales
Understanding Order of Magnitude
What is Order of Magnitude?
An order of magnitude is a way to express the scale or size of a number using powers of 10. It provides a rough estimate of how large or small a number is without worrying about the exact digits.
Scientific Notation Format
a = b x 10ⁿ- a: Original number
- b: Coefficient (1 ≤ |b| < 10)
- n: Exponent (order of magnitude)
How to Calculate
Step 1: Take Absolute Value
Work with |a| to handle negative numbers
Step 2: Find Logarithm
Calculate log₁₀(|a|)
Step 3: Take Floor
n = floor(log₁₀(|a|))
Worked Example
Find order of magnitude of 2800:
1. |2800| = 2800
2. log₁₀(2800) = 3.447
3. floor(3.447) = 3
4. Scientific notation: 2.8 x 10³
Order of magnitude: 3
Applications
Science
Comparing scales from atoms to galaxies
Engineering
Quick estimates and feasibility checks
Economics
Comparing financial scales and budgets
Data Analysis
Understanding data ranges and distributions