# Order of Magnitude Calculator

URL: https://speedycalculator.com/calculators/math/order-of-magnitude/
Last updated: 2026-10-30

> The order of magnitude calculator writes a number in scientific notation and gives its order of magnitude – the power of ten n in a × 10ⁿ.

## Inputs

- Number

## Results

- Order of magnitude
- Scientific notation
- E-notation

## Formula

```
x = a × 10ⁿ with 1 ≤ |a| < 10;  order of magnitude = n
```

## Explanation

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.

## 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.

## FAQ

**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).


## Sources

- [OpenStax – Prealgebra 2e](https://openstax.org/details/books/prealgebra-2e)
- [Wolfram MathWorld – Order of magnitude](https://mathworld.wolfram.com/OrderofMagnitude.html)