The E-series steps by 10^(1/n) per decade, sized so that consecutive tolerance bands overlap. E24 steps by 1.10 and carries 5%, which spans 1.11 — so every value in the decade is already covered, and a 5k resistor would be indistinguishable from the 5.1k next to it.
It explains a numbering system that otherwise looks arbitrary, and it changes how you shop. Asking for a value that is not in the series is usually pointless rather than unlucky: the nearest stocked part, with its tolerance, very often contains the number you wanted. Knowing the spacing also tells you immediately which series you need — if your circuit cares about 2%, E24 cannot express it and E96 can.
The tidy story is an idealisation. Published values are rounded to two or three figures, and rounding widens some steps past what the tolerance can bridge — E12 jumps from 12 to 15, a ratio of 1.25 against a 1.22 span, so a 1.34k target is more than 10% from both neighbours. Small holes exist in every series, including the coarse ones.
Estimate with the rule, then check it against the calculator that models it properly.
Open Resistor Colour Code Calculator →The E-series steps by 10^(1/n) per decade, sized so that consecutive tolerance bands overlap. E24 steps by 1.10 and carries 5%, which spans 1.11 — so every value in the decade is already covered, and a 5k resistor would be indistinguishable from the 5.1k next to it. It explains a numbering system that otherwise looks arbitrary, and it changes how you shop.