Poisson Process Calculator
Free online poisson process 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：泊松过程计算器
原理：泊松过程是无记忆的随机事件流——事件在任意时刻等可能发生、互不影响。时长 t 内的事件数服从泊松分布 P(N(t)=k) = e⁻ᐧλt·(λt)ᵏ/k!，相邻事件间隔服从指数分布。网页访问、客服来电、放射性衰变计数都近似这一模型。
步骤：① 输入事件率 λ 与时长 t；② 给出感兴趣的事件数 k；③ 点击计算。
示例：λ = 2、t = 3 时期望 6 个事件，恰好发生 4 个的概率 0.13385261754，不超过 4 个的概率 0.285056500317。
注意事项：模型要求事件独立且率恒定——高峰时段的来电率会变化，应分段建模；泊松分布的方差等于均值 λt，实际数据若方差明显偏大说明存在聚集（可用负二项修正）；k 较大时用连续近似避免数值下溢。
相关：泊松分布计算器给出单参数版本；指数分布计算器描述事件间隔；放射性衰变计算器是泊松过程在物理中的直接应用。
How to use the Poisson Process 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 Poisson Process 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 2026-10-05
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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