Orders of magnitude make enormous ranges understandable: an atom is about 10⁻¹⁰ m across and the Earth about 10⁷ m, 17 orders of magnitude apart. Scientists use them for quick “Fermi” estimates.
How to use the Order of Magnitude Calculator
- Number
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
The calculator reads the digits exactly, finds the position of the first non-zero digit and moves the decimal point after it; the number of places moved is n.
Formula
x = a × 10ⁿ with 1 ≤ |a| < 10; order of magnitude = n
Worked example
Inputs — Number: 0.00045.
Results — Order of magnitude = -4; Scientific notation = 4.5 × 10⁻⁴; E-notation = 4.5e-4.
Key terms
- Order of magnitude
- The power of ten that sets a number's scale.
Frequently asked questions
What is the order of magnitude of 5,000?
3, because 5,000 = 5 × 10³.
What about numbers below 1?
They have negative orders: 0.002 = 2 × 10⁻³.
Do two numbers with the same order have similar sizes?
Within a factor of 10.
Is 9,999 the same order as 1,000?
Yes, 3 – although some define the order by rounding log₁₀(x).