SNORM.DIST.RANGE Function (Gnumeric)

• Introduction: Gnumeric 1.12.3. NEWS explicitly adds SNORM.DIST.RANGE.
• Source support: Registered in the Gnumeric 1.12.62 plugin. No retirement is established. The last functioning application version is unverified for this guide.
• Evidence dates: Official source was retained October 13–14, 2026 and reviewed October 15. Independent exact-rational and high-precision mathematical checks are reference calculations. No native Gnumeric, headless application, GUI or random-generator execution was performed.

=SNORM.DIST.RANGE(x1,x2)

Both arguments are required. The function integrates the standard-normal density from x1 to x2. Its mathematical definition is Phi(x2)-Phi(x1), where Phi is the cumulative distribution with mean zero and standard deviation one.

When x1 is below x2, the result is the mass between them. Equal limits return zero. Reversed limits produce the negative of the forward integral, as both the help and the helper specify. A negative result is therefore possible without an error: it usually signals reversed bounds if the intended output was a probability.

The inputs are standardized values, not arbitrary measurements. A raw value of 100 means one hundred standard deviations above zero in this function. To describe another normal model, first subtract its mean and divide by its positive standard deviation.

Create NormalIntervals with Lower in A1, Upper in B1 and Mass in C1. Enter the first six interval pairs from the reference table below into A2:B7. Fill C2 =SNORM.DIST.RANGE(A2,B2) downward. The first rows provide central intervals, a one-sided interval starting at zero, a positive interval, its reversal and equal endpoints.

For a controlled change, replace the first row’s bounds -1 and 1 with -2 and 2 in a copy. Its mass changes from approximately 0.682689492137 to 0.954499736104. Widening this nested interval adds mass. It does not make the model appropriate for data that are not normally distributed.

Values are independent high-precision integrals, rounded for display. They are not native Gnumeric captures or a promise that every runtime backend reproduces all shown digits. The narrow-interval row treats its displayed decimal endpoints as exact mathematical numbers; spreadsheet literal arithmetic can represent a slightly different width.

Suppose a specified model has mean 100 and standard deviation 15. Put those values in F2 and G2, lower bound 85 in H2 and upper bound 115 in I2. Use =SNORM.DIST.RANGE((H2-F2)/G2,(I2-F2)/G2) in J2. The standardized limits are -1 and 1, giving 0.682689492137.

In a copy change H2:I2 to 100,130. The standardized limits become 0 and 2; the mass is 0.477249868052. This is an interval probability under the specified model, not a prediction that exactly that fraction of a finite sample must fall inside the interval.

Do not divide by a negative or zero standard deviation when adapting this workflow. The interval function itself has no mean or scale argument and cannot validate a separate model’s scale for you. Keep units consistent across the measurement, mean and standard deviation.

Compute the masses for [-2,-1], [-1,1] and [1,2] in separate rows. Their sum is approximately 0.954499736104, matching the [-2,2] result. The outside intervals each have mass 0.135905121983 because the density is symmetric about zero.

As a sign control, add the results for [1,2] and [2,1]. The mathematical sum is 0, not twice the positive probability. Keeping this test beside a parameterized calculation helps catch reversed inputs before interpreting an output as a proportion.

The pinned implementation calls pnorm2. For positive intervals that helper starts with upper-tail probabilities, avoiding a direct subtraction of two cumulative values both close to one. In a sufficiently narrow interval it also uses endpoint-density bounds to constrain the subtraction result. This source design is relevant to tail and narrow-interval calculations, but it is not an independent native accuracy certificate.

For [8,9], the reference mass is about 6.219831985866e-16. Fixed twelve-decimal formatting would display zero even though the mathematical value is positive. Use scientific notation when the magnitude matters. Subtracting displayed rounded cumulative probabilities is particularly unsuitable for this case.

For the vendor-style interval from 0.6 to 0.6+1e-10, the nominal decimal-width integral is approximately 3.332246028818e-11. The actual stored difference between two floating-point endpoints may differ from exactly 1e-10. Separate that input-representation effect from the helper’s integration error when comparing very small quantities.

Numeric argument errors propagate. Negative limits are valid standardized inputs, while reversed limits intentionally give a negative integral. Text parsing, array behavior, literal infinities, extreme overflow/underflow and native precision across all builds were not executed.

If a result is unexpectedly negative, check argument order first. If it appears to be zero, inspect the number format and interval width. If it is unexpectedly tiny, confirm that raw measurements were standardized. A correct reference integral does not validate the normality assumption or certify a statistical decision.

• Function-specific help and worksheet callback
• Pinned pnorm2 interval implementation
• Gnumeric official function catalogue

NORMSDIST, STANDARDIZE, NORMDIST.