Q Function Calculator
Free online q function 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：Q 函数计算器（正态右尾概率）
Q 函数 Q(x) = 1 − Φ(x) = 0.5·erfc(x/√2)，是标准正态分布的右尾概率。通信工程用它写误码率：BPSK 相干解调 Pe = Q(√(2·SNR))，雷达检测、假设检验的 p 值换算、半导体良率也都落在它身上。
工程速记：Q(3) ≈ 0.00135 是「3σ 单侧」，Q(1.96) ≈ 0.025 是 95% 置信的尾巴。深尾部（x 大于 6）用 erfc 连分式计算避免灾难性消去，保证 12 位有效数字。
参考值
Q(1) = 0.158655253931457，Q(1.96) = 0.0249978951482204，Q(3) = 0.00134989803163009
Q(5) = 2.86651571879194e−7，Q(10) = 7.61985302416047e−24
How to use the Q Function 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 Q Function 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 2026-09-27
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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