Rationalise denominator (1/sqrt(n)) calculator

Reviewed by the CalculatorHub team, edited by James Graham. Method: a standard formula rather than a jurisdiction-specific rule. How we document and test our methods. Last verified 2026-07-09.

The Rationalise denominator (1/sqrt(n)) calculator computes rationalise denominator (1/sqrt(n)) from the relation 1/sqrt(n) = sqrt(n)/n. It takes a single input (n under root) and returns the decimal value. These calculators suit students and teachers working through the steps of a problem, and analysts, technicians and anyone else who needs an intermediate value before moving on to the next stage of a longer calculation or writing the figure into a report. Enter your values below and the result updates instantly, and you can share a permalink that pre-fills the exact calculation. Enter each value at the full precision you have and round only at the end, because rounding partway through can move the final digits of the answer; where two quantities are compared, put them on the same scale and in the same units first, and keep track of which input goes in which field, since many of these formulas treat their inputs differently and swapping two entries can change the result. For example, with n under root = 1, the decimal value works out to 1, and the worked example further down the page shows every step so you can follow the arithmetic and reproduce it by hand. This is a standard formula rather than a jurisdiction-specific rule, so it does not depend on an external rate or schedule, and the figure above each result carries the date it was last verified. A result is exact only for inputs inside the operation's defined domain, since a denominator cannot be zero and some functions accept only positive arguments or have no real value outside a limited range; and where the true value does not terminate, as with an irrational root or a repeating decimal, the figure shown is that number rounded to the digits displayed rather than the exact value.