Order of Magnitude Calculator — Power of 10
Enter any number to instantly find its order of magnitude — the integer n such that |x| ≈ 10ⁿ — together with the full scientific notation and the nearest powers of 10 above and below your value.
The exponent n such that |x| ≈ 10ⁿ
- 1
Absolute value |x|
|52,000| = 52,000 - 2
log₁₀(|x|)
log₁₀(52,000) = 4.716003 - 3
Order of magnitude = ⌊log₁₀(|x|)⌋
⌊4.716003⌋ = 4The floor function rounds down to the nearest integer, giving the power of 10.
How does this calculator work?
Order of magnitude = floor(log₁₀(|x|)): the integer exponent n such that 10ⁿ ≤ |x| < 10^(n+1). Divide |x| by 10ⁿ to get the coefficient (between 1 and 10) for scientific notation. Negative numbers and decimals are supported; zero has no order of magnitude.
Formula
How this is calculated
The order of magnitude of a number is the integer part of its base-10 logarithm: OOM(x) = floor(log₁₀(|x|)). For x = 52 000, log₁₀(52 000) ≈ 4.716, so OOM = 4 — meaning 52 000 lives in the ten-thousands range. For x = 0.0034, log₁₀(0.0034) ≈ −2.47, so OOM = −3 — the thousandths range.
Scientific notation expresses any number as coefficient × 10^n, where 1 ≤ |coefficient| < 10 and n is the order of magnitude. The coefficient is found by dividing the absolute value by 10^OOM. For 52 000 this gives 52 000 / 10 000 = 5.2, so the full notation is 5.2 × 10⁴.
Order of magnitude is widely used in science and engineering to compare quantities that differ by many powers of 10 (e.g. atomic radii ≈ 10⁻¹⁰ m vs. the observable universe ≈ 10²⁶ m). Two quantities are said to be "the same order of magnitude" if their ratio is less than 10 — they share the same first digit in the list …, 0.001, 0.01, 0.1, 1, 10, 100, …
Frequently asked questions
log₁₀(1 000 000) = 6, so the order of magnitude is 6. The number is expressed in scientific notation as 1.0 × 10⁶.
Yes. Numbers between 0 and 1 have negative orders of magnitude. For example, 0.0045 has OOM = floor(log₁₀(0.0045)) = floor(−2.35) = −3, placing it in the thousandths range.
log₁₀(0) is undefined (it approaches −∞). Zero has no meaningful order of magnitude — it is not expressible as any power of 10.
Also known as
TG we-Calculate Editorial Team. (2026). Order of Magnitude Calculator — Power of 10 [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/order-of-magnitude-calculator
TG we-Calculate Editorial Team. "Order of Magnitude Calculator — Power of 10." TG we-Calculate. 2026. https://we-calculate.com/calculator/order-of-magnitude-calculator.
TG we-Calculate Editorial Team, "Order of Magnitude Calculator — Power of 10," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/order-of-magnitude-calculator
@misc{wecalculate_order_of_magnitude_calculator, title = {Order of Magnitude Calculator — Power of 10}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/order-of-magnitude-calculator}}, year = {2026}, note = {TG we-Calculate} }
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