is an implementation of arithmetic operators for Rational numbers

A Rational is a number that can be expressed as a fraction of two integers. It includes also repeating decimals hence is a super-set of floating point numbers.


With npm do

npm install arithmetica

This package is implemented with ECMAScript modules. CommonJS is not supported, nor bundle is provided.

If you need a bundle, for example only with floating point operators (i.e. without repeating decimals) you can do something like.

git clone
cd arithmetica
esbuild --bundle float/index.js --minify --outfile=arithmetica.js

It will produce a 1.6kb (minified, not gzipped) arithmetica.js file.


import { add } from "arithmetica";

add("1", "2"); // '3'

// Here 0._3 represents 0.3333333333333333...
add("0._3", "1")); // '1._3'

NOTA BENE: there is no runtime check on types: consumers are responsible to feed inputs that are actual Rational types, for instance using isRational type-guard.

If you want only floating point operators, without repeating decimals support, you can do

import { add } from "arithmetica/float";

add("0.1", "0.2"); // '0.3'



A Float is a string that expresses a decimal representation of a number.

Decimal separator is “.” character. Exponential notation is not allowed. Integer part can be omitted.

For example:


A Rational includes every Float plus repeating decimals that are decimal representation of a number whose digits are periodic.

A repeating decimal is represented by a string like:

Type guards


isFloat(arg: unknown): arg is Float

Use isFloat type-guard to check if some data belongs to Float type.

import { Float, isFloat, sub } from "arithmetica/float";

function minusOne (a: string): Float {
  if (isFloat(a)) return sub(a, "1");
  throw new TypeError(`Argument is not a Float ${a}`);

Of course it can be used also on an ECMAScript runtime.

import { isFloat, mul } from "arithmetica/float";

function timesTen (a) {
  if (isFloat(a)) return mul(a, "10");
  throw new TypeError("Argument is not a Float");


isRational(arg: unknown): arg is Rational

Use isRational type-guard to check if some data belongs to Rational type.

import { Rational, isRational, add } from "arithmetica";

function plusOneThird (a: string): Rational {
  if (isRational(a)) return add(a, "0._3");
  throw new TypeError(`Argument is not a Rational ${a}`);


Every operator imported from arithmetica/float has the same signature as its homonym operator imported from arithmetica, but of course with type Float instead of a Rational in its signature.


Implements equality operator.

eq(a: Rational, b: Rational): boolean

import { eq } from "arithmetica";

eq("1", "2"); // false
eq("42", "42.0"); // true


Implements addition operator.

add(a: Rational, b: Rational): Rational

import { add } from "arithmetica";

add("1", "2"); // '3'
add("0._1", "0._1"); // '0._2' i.e. 0.2222222...
add("0._1", "0._8"); // "1"


Implements subtraction operator.

sub(a: Rational, b: Rational): Rational

import { sub } from "arithmetica";

sub("1", "2"); // '-1'
sub("0._1", "0._1"); // '0'
sub("1", "0._1"); // "0._8"


Implements negation operator.

neg(a: Rational): Rational

import { neg } from "arithmetica";

neg("1"); // '-1'
neg("-42"); // '42'


Implements multiplication operator.

mul(a: Rational, b: Rational): Rational

import { mul } from "arithmetica";

mul("2", "-3"); // '-6'
mul("0._3", "0.3"); // '0.1'


Implements division operator.

div(a: Rational, b: Rational): Rational

It throws RangeError if denominator is zero.

import { div } from "arithmetica";

div("-10", "2"); // '-5'

try {
  div("2", "0");
} catch (err) {
  console.error(err); // RangeError: Division by zero


Implements inversion operator.

inv(a: Rational): Rational

import { inv } from "arithmetica";

inv("2"); // '0.5'
inv("1._1"); // '9'


Implements less then operator.

lt(a: Rational, b: Rational): boolean

import { lt } from "arithmetica";

lt("-2", "1"); // true


Implements greater then operator.

gt(a: Rational, b: Rational): boolean

import { gt } from "arithmetica";

gt("-2", "1"); // false
gt("42", "24"); // true



Coerces to Float.

coerceToFloat(arg: unknown): Float

import { coerceToFloat } from "arithmetica/float";

coerceToFloat(0); // '0'
coerceToFloat(-1.23); // '-1.23'


Converts a Float to a number.

floatToNumber(floatStr: Float, mantissaLength?: number): number

import { floatToNumber } from "arithmetica/float";

floatToNumber("42.01", 0); // 42
floatToNumber("1234.56789", 2); // 1234.57


Coerces to Rational.

coerceToRational(arg: unknown): Rational

import { coerceToRational } from "arithmetica";

coerceToRational(42); // '42'
coerceToRational(-1n); // '-1'


Converts a Rational to a number.

rationalToNumber(rational: Rational, mantissaLength?: number): number

Notice that mantissaLength argument is optional: it set the number of digits of the decimal part, max is 16. Output is rounded.

import { rationalToNumber } from "arithmetica";

rationalToNumber("0.10"); // 0.1
rationalToNumber("0._3", 8); // 0.33333333
rationalToNumber("0.456", 2); // 0.46