What does "operations" mean here?

Operations represent the number of basic steps (comparisons, swaps, accesses) an algorithm performs, as predicted by its Big-O formula. Constants and lower-order terms are ignored — Big-O gives the dominant growth term.

Why is O(n!) capped at n=20?

20! is about 2.4 × 10^18 operations. At n=21 the value exceeds safe integer range and loses precision. In practice, factorial algorithms are infeasible for n > 12 anyway.

Why does O(1) always show 1?

Constant time means the algorithm takes the same number of steps regardless of input size — array index lookup and hash-map access are typical examples.

What is a realistic upper limit for n²?

Modern hardware can execute roughly 10^8–10^9 simple operations per second. For O(n²), n=10,000 means 10^8 operations — about 1 second. n=100,000 means 10^10 — too slow for most interactive use cases.

Can this analyze my code's complexity automatically?

No — it does not parse source code. Identify your algorithm's Big-O class from its loops and recursion, then read the operation count for your input size here.

Time Complexity Calculator

Name: Time Complexity Calculator
Availability: InStock
Author: Nham Vu

Enter an input size n and instantly see the exact operation count for each Big-O complexity class in a side-by-side comparison table.

Calculate Operation Counts

Enter an input size n to see how many operations each complexity class requires.

Input size n

Factorial capped at n = 20 due to numeric limits.

Operation Counts for n = 100

Sorted fastest to slowest

Complexity	Class name	Operations	Approx.	Feasibility

Multi-n Comparison

* Values shown as approximate counts. Factorial and exponential capped at n = 20.

Summary

Enter an input size n and instantly see the exact operation count for each Big-O complexity class in a side-by-side comparison table.

How it works

Enter an input size n (up to 10,000 for polynomial classes; capped at 20 for exponential and factorial).
The calculator evaluates each Big-O formula — 1, log2(n), n, n×log2(n), n², 2^n, n! — for that n.
Each row shows the exact operation count with a color-coded feasibility label.
Compare the classes side by side to judge which algorithms stay practical at your data size.

Use cases

Estimate whether a brute-force O(n²) approach is fast enough before optimizing.
Decide between O(n log n) merge sort and O(n²) insertion sort for a given dataset size.
Determine at what n an exponential-time algorithm becomes computationally infeasible.
Quickly calculate exact operation counts during algorithm design and code review.
Teach Big-O trade-offs by showing concrete numbers side-by-side.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu