The chi-square test compares observed vs. expected frequencies.
χ² = Σ (O − E)² / E
Reach for this calculator when you need a result you can act on confidently. The formula is straightforward, but manual computation introduces rounding errors that this tool eliminates entirely.
A common mistake is applying the formula in the wrong direction — particularly with percentage and ratio problems, where the part and the whole can be mistakenly swapped. Check which value is the reference (the 'whole') before entering inputs.
A shopper sees two versions of the same product at different prices: one at £14.50 for 400g and another at £11.99 for 300g. Running both price-per-gram calculations reveals the larger pack is 7% cheaper per unit — the kind of comparison that is impossible to do reliably in your head at the shelf.
For categorical data to test if distribution matches expected values.