Algorithm Complexity Calculator
Compare two complexity classes to find the input size where the better one wins.
About Algorithm Complexity Calculator
Big-O hides constant factors, which is why a theoretically worse algorithm often wins on small input. Insertion sort beating quicksort below about a dozen elements is the classic example, and real sort implementations exploit exactly that. Choosing an algorithm requires knowing the expected input size, not just the asymptotic class.
Formula
Algorithm Complexity
Operations = constant factor × growth function of n, compared across the two algorithms
- constant factor
- Per-operation overhead that big-O notation deliberately ignores
Worked example
With the default values below, Algorithm Complexity Calculator returns Faster Algorithm at This Size of Algorithm B. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Input size nminimum 1
- 5,000
- Algorithm A complexityone of O(1) constant, O(log n) logarithmic, O(n) linear, O(n log n) linearithmic, O(n squared) quadratic, O(n cubed) cubic, O(2 to the n) exponential
- O(n squared) quadratic
- Algorithm B complexityone of O(1) constant, O(log n) logarithmic, O(n) linear, O(n log n) linearithmic, O(n squared) quadratic, O(n cubed) cubic, O(2 to the n) exponential
- O(n log n) linearithmic
- Constant factor of Aminimum 0.001 x
- 1 x
- Constant factor of Bminimum 0.001 x
- 8 x
Results
- Faster Algorithm at This Size
- Algorithm B
- Operations for A
- 25,000,000
- Operations for B
- 491,508
- Speed Advantage
- 50.864 x
- Guidance
- The ranking reverses between small and large input — the constant factor dominates when n is small
Step by step
- 1Values used
- 2Algorithm Complexity
- 3Faster Algorithm at This Size= Algorithm B
- 4Operations for A= 25,000,000
- 5Operations for B= 491,508
- 6Speed Advantage= 50.864 x
- 7Guidance= The ranking reverses between small and large input — the constant factor dominates when n is small
Assumptions and limits
- The result is derived only from the 5 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 3 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
How is Algorithm Complexity calculated?
Operations = constant factor × growth function of n, compared across the two algorithms Big-O hides constant factors, which is why a theoretically worse algorithm often wins on small input. Insertion sort beating quicksort below about a dozen elements is the classic example, and real sort implementations exploit exactly that.
Why does Algorithm Complexity matter?
Choosing an algorithm requires knowing the expected input size, not just the asymptotic class.
What values do I need to enter?
This calculator takes 5 inputs: Input size n, Algorithm A complexity, Algorithm B complexity, Constant factor of A, Constant factor of B. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.