Find the interval that contains a stated proportion of the population at a stated confidence. Paste your data (or enter mean, SD and n), choose coverage and confidence, and get the interval, the k-factor and a nonparametric option — all client-side.
Enter your data, choose coverage and confidence, then press Calculate to find the tolerance interval.
You want a range that captures, say, 99% of all product — not just the average. Enter the lab to build a tolerance interval.
Paste a single column of measurements, or switch to summary mode and type the mean, standard deviation and sample size. Then choose how much of the population to cover (e.g. 99%) and your confidence level (e.g. 95%).
The calculator finds a special multiplier (k-factor) based on your sample size, how much of the population you want to cover, and your confidence level. This multiplier is what converts your average and spread into a practical range.
That range is built from your average, spread, and the k-factor. If you've entered spec limits, the calculator checks whether the range fits inside them and tells you whether your process is expected to meet spec. A nonparametric option builds the range from your actual min and max instead.
A tolerance interval tells you where most individual values in a population fall — not just the average. It is the right tool when you need to say, with stated confidence, that a stated proportion of all parts (for example 99% of them) will lie inside a range, and to check that range against your specification limits.
A tolerance interval is a range, computed from a sample, that is expected to contain a stated proportion of the entire population with a stated confidence. For example, "we are 95% confident that 99% of all parts will measure between 43.3 mm and 56.7 mm." Unlike a confidence interval (which is about the mean) or a prediction interval (about the next value), a tolerance interval is about the bulk of the individual items.
A tolerance interval gives a range expected to contain a chosen percentage of the entire population — say 99% of all units — with a stated confidence. That is different from a confidence interval, which only brackets the average. For normal data it takes the form 'average plus or minus k times the standard deviation', where the factor k grows with the coverage and confidence you ask for and shrinks as your sample gets larger. If you would rather not assume a normal shape, the nonparametric option simply uses your smallest and largest observed values as the bounds.
An engineer measures 30 parts and wants a specification that covers 99% of all future production with 95% confidence. Sample mean: 50.2mm. Standard deviation: 0.4mm.
The tolerance interval gives 48.8mm to 51.6mm — wider than a simple ±2σ because it accounts for the fact that 30 samples don't perfectly represent the full population.
What to do with this: Set spec limits at 48.8–51.6mm. If the customer spec is tighter, you know upfront that you'll have rejects — fix the process before committing to delivery dates.
Tolerance intervals answer the question customers and auditors really ask: "will almost all of my parts meet spec?" They turn a sample of a few dozen measurements into a defensible statement about the whole population, which is the basis for setting realistic specifications, releasing batches, and demonstrating capability.
Use a tolerance interval in the Measure and Analyse phases to set or validate specification limits, in the Control phase to confirm that a stable process keeps most output inside spec, and in supplier qualification to show that the bulk of incoming material conforms. Choose one-sided when only an upper or lower limit matters (e.g. impurity, strength).
Tolerance intervals complement capability indices (Cp, Cpk). Where Cpk summarises capability in one number, the tolerance interval states explicitly where most of the population lies and with what confidence — making it ideal for spec-setting, design verification and risk-based release decisions.
Compare the tolerance interval to your specification limits. If it sits comfortably inside, you have evidence that most output will conform; document it in your control plan. If it spills outside, you need to reduce variation, re-centre the process, or widen the spec (with customer agreement). Pair the result with a capability study and a control chart so you can show that the process is both capable and stable over time.
Combine tolerance intervals with capability analysis, control charts, and a DMAIC project structure to set specs and verify conformance.
A confidence interval gives a plausible range for a single parameter such as the population mean. A prediction interval gives a range for the next single observation. A tolerance interval is wider than both: it gives a range that contains a stated proportion of the whole population (for example 99% of all parts) at a stated confidence (for example 95%). Use a tolerance interval when you need to make a statement about where most individual values fall, not just the average.
For a normal tolerance interval the limits are x̄ ± k·s, where x̄ is the sample mean, s is the sample standard deviation, and k is the tolerance factor. The k-factor depends on three things: the sample size n, the proportion of the population you want to cover, and the confidence level. This calculator uses the standard Howe approximation for two-sided intervals and the Natrella approximation for one-sided intervals. A larger k makes a wider interval — k grows when you ask for more coverage, higher confidence, or have a smaller sample.
Sample size has a strong effect. With few data points the k-factor is large and the interval is wide, because there is great uncertainty in the estimated mean and standard deviation. As n increases the k-factor shrinks toward the pure normal quantile (for example about 2.576 for two-sided 99% coverage), and the interval narrows. As a rough guide, aim for at least 30 measurements for a usable normal tolerance interval, and more if you need high coverage and high confidence.
Use the nonparametric option when your data is not normally distributed, or when you do not want to assume any distribution. It uses the smallest and largest observed values (order statistics) as the interval, and reports the confidence actually achieved for your chosen coverage. The trade-off is that you need a lot of data: covering 99% of the population with 95% confidence using the min and max requires roughly 473 observations, so the normal method is far more efficient when the normality assumption holds.
A tolerance interval shows where most of your population lies. Structured training shows you how to set specs, prove capability, and sustain it.
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