Forecast Accuracy Confidence Interval Calculator

The Forecast Accuracy Confidence Interval Calculator estimates a confidence interval around an observed forecast accuracy rate. Instead of treating the sample rate as exact, it shows a plausible range for the underlying rate when you have evaluated only part of the full workload.

This is useful when forecast evaluation teams review monitoring samples, validation runs, or audit batches and need to communicate uncertainty alongside a headline percentage. The calculator uses the Wilson score interval, which generally behaves better than a simple normal interval when the sample is modest or the observed rate is near 0% or 100%. Use the interval to compare runs, set review thresholds, or decide whether more observations are needed before acting.

Rate estimation inputs

Forecasts evaluated

Accurate forecasts

Confidence level

Result

—

Observed rate

Lower bound—

Upper bound—

Sample size—

How to use

1. Enter forecasts evaluated

Provide the number of independent observations included in the evaluation. Use the count actually checked, not the full production population unless every item was reviewed.

2. Enter accurate forecasts

Enter how many of those observations met the definition of success used by your team. The count cannot exceed the total.

3. Choose a confidence level

Select 90%, 95%, or 99%. A higher confidence level produces a wider interval because it requires more statistical certainty.

4. Review the estimated rate

The main result shows the observed percentage from the sample.

5. Check the interval bounds

Use the lower and upper bounds to understand sampling uncertainty. Wider intervals indicate less precision.

Formula

p̂ = x / n center = (p̂ + z²/(2n)) / (1 + z²/n) half-width = z × √((p̂(1−p̂) + z²/(4n))/n) / (1 + z²/n) Wilson interval = center ± half-width

Where:

x = number of accurate forecasts
n = number of forecasts evaluated
p̂ = observed success proportion
z = critical value for the selected confidence level

Assumptions: Observations are treated as independent and the success rule is applied consistently. The interval quantifies sampling uncertainty only; it does not correct labeling mistakes, drift, bias, or dependence between observations.

What the result means

The main result is a planning estimate for forecast accuracy confidence interval. Use the supporting values to understand how the result was formed and compare scenarios consistently.

Statistical estimate only; define the success criterion consistently before interpreting results.

Example calculation

Given:

Forecasts evaluated: 240
Accurate forecasts: 210
Confidence level: 95% (z = 1.96)

Calculation:

Observed rate = 210 / 240 = 87.50%
Wilson center = 86.91%
Half-width = 4.19 percentage points
Interval = 82.72% to 91.10%

Result: 87.50% observed rate; 95% CI 82.72%–91.10%.

Interpretation: The sample rate is the point estimate, while the interval shows the range supported by the sample under the model. A larger sample would usually narrow the interval if the rate stays similar.

FAQ

Why is the confidence interval not centered exactly on the observed rate?

The Wilson method adjusts both the center and width, especially for smaller samples or rates near the boundaries. That behavior avoids some weaknesses of the basic p ± z√(p(1−p)/n) interval.

Should I enter percentages or counts?

Enter counts for the total and successful observations. The calculator converts them to a percentage internally, which avoids rounding error from entering a pre-rounded rate.

Does a 95% interval mean there is a 95% probability the true rate is inside this one interval?

Not in the frequentist interpretation used here. The 95% refers to the long-run coverage of intervals produced by the same procedure across repeated samples.

What if every checked item passes or every item fails?

The Wilson interval still returns a finite range rather than collapsing to 0% or 100%. That is one reason it is useful for boundary cases.

How is this different from an error rate estimator?

A confidence interval focuses on uncertainty around a rate. An error rate estimator focuses on the observed share of failures itself, usually without adding an uncertainty range unless requested separately.

Related tools