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Big O Growth Comparison Calculator

Work out big o growth comparison instantly with clear inputs, formula shown and shareable results.

About Big O Growth Comparison Calculator

Big-O describes how work scales with input size. Comparing two classes at a concrete n shows the practical gap: the ordering 1 < log n < n < n log n < n² < n³ < 2ⁿ holds for all sufficiently large n.

Formula

Growth ordering

O(1) ⊂ O(log n) ⊂ O(n) ⊂ O(n log n) ⊂ O(n²) ⊂ O(n³) ⊂ O(2ⁿ)

Worked example

With the default values below, Big O Growth Comparison Calculator returns Second ÷ first of 100.343332. Change any input above and every figure here is recalculated in your browser.

Inputs used

Input size naccepts 1–1,000,000
1,000
First complexityone of O(1), O(log n), O(n), O(n log n), O(n²), O(n³), O(2ⁿ)
O(n log n)
Second complexityone of O(1), O(log n), O(n), O(n log n), O(n²), O(n³), O(2ⁿ)
O(n²)

Results

Second ÷ first
100.343332
Operation count for the first
9,965.78
Operation count for the second
1,000,000.00
Which grows more slowly
The first complexity is faster

Step by step

  1. 1Values used
  2. 2Growth ordering
  3. 3Second ÷ first= 100.343332
  4. 4Operation count for the first= 9,965.78
  5. 5Operation count for the second= 1,000,000.00
  6. 6Which grows more slowly= The first complexity is faster

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

n log n versus n² at n = 1000?

About 9966 against 1000000 — the quadratic algorithm does roughly 100 times more work.

Do constants matter?

Big-O ignores them, but in practice a large constant can make an asymptotically better algorithm slower for small inputs.

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