A 类标准不确定度计算器

Type A Standard Uncertainty Calculator

Compute u_A = s/√n from sample standard deviation and the number of independent measurements (statistical evaluation).

📐 计算公式
A 类标准不确定度(本页代码口径):u_A=样本标准差 s÷√测量次数 n;联动量:回算标准差=u_A×√n、u_A 占标准差比=u_A÷max(s,10⁻¹²)×100(%)、u_A 倒数。校验:两字段经输入守卫必填且须为合法数值,否则提示并中止。判据:无固定分级,u_A 随测量次数按平方根缩减,次数增至 4 倍不确定度减半。

输入样本标准差 s 与测量次数 n,求 A 类标准不确定度。

Formula & Standard References

Item Formula / Note Source / Standard
Type A standard uncertainty u_A = s / sqrt(n), the experimental standard deviation of the mean JCGM 100:2008, Guide to the Expression of Uncertainty in Measurement (GUM)
Experimental standard deviation s = sqrt( sum(x_i - xbar)^2/(n-1) ) from n independent observations JCGM 100:2008, Guide to the Expression of Uncertainty in Measurement (GUM)
Degrees of freedom nu = n - 1, used to fix the coverage factor and confidence level JCGM 100:2008, Guide to the Expression of Uncertainty in Measurement (GUM)
Combining with Type B u_c = sqrt(u_A^2 + u_B^2), combining both types in quadrature JCGM 100:2008, Guide to the Expression of Uncertainty in Measurement (GUM)
📌 计算说明
  • u_A = s/√n(多次重复测量)。
  • s=2,n=9 → 0.6667。

📚 深度解析:A 类标准偏差

💡 常见使用场景

公式
s = sqrt(sum((xi-xbar)^2)/(n-1))。例:5 次测 10.001,10.003,9.999,10.002,10.000,s≈0.0016。
样本标准差 1.5,测量次数 16
u_A=s/√n=1.5/4=0.3750。测量次数翻倍只能把 u_A 降到约 70%,靠增加 n 降低不确定度的收益递减。

❓ 常见问题(FAQ)

A 类定义?
用统计法(重复观测)评定的不确定度分量。
与 B 类?
B 类用非统计信息(证书/经验/手册)。