Stirling Approximation Calculator
Free online stirling approximation calculator. Enter your values and get instant results with the formula, step-by-step working, a worked example and FAQs — everything runs locally in your browser on Calcton, no signup required.
中文版：斯特林近似计算器
斯特林近似 n! ≈ √(2πn)·(n/e)ⁿ。大数阶乘直接计算会溢出，工程上在对数域比较：ln n! ≈ n·ln n − n + 0.5·ln(2πn) + 1/(12n)，修正项使相对误差降到 1/(12n²) 量级。
基本斯特林在 n = 10 时相对误差约 8%，加 1/(12n) 修正后降到约 0.8%；误差按 1/(12n²) 衰减，n = 100 时修正后已低于 0.01%。典型应用：二项系数与大 n 组合计数、统计力学熵 S = k·ln W、比较排序下界 Ω(n log n) 的证明。
How to use the Stirling Approximation Calculator
- Fill in the inputs with your own numbers — every field shows what it expects.
- The result updates instantly as you type; no "Calculate" click needed.
- Read the result card for the main figure, the step-by-step formula, and practical notes.
Frequently asked questions
Is the Stirling Approximation Calculator free?
Yes — all math calculators on Calcton are free, with no sign-up required. Your inputs are processed in your browser and never sent to a server.
Is there a Chinese version of this tool?
Yes. Use the Chinese version link above — it is the same calculator with the interface in Simplified Chinese.
References
Formulas and benchmarks used by this calculator follow these published sources.
KevinContent LeadCalcton Editorial Team · Last updated 2026-09-12
Kevin maintains Calcton's formula verification and content: every calculator cites the standard it implements, worked examples are recomputed programmatically, and health benchmarks follow WHO and international guidelines.
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