Opposite Reciprocal Calculator

Find the negative reciprocal of any number or slope quickly here. Enter decimals, fractions, mixed numbers, or undefined, and get explanations and steps. See fraction form, simplified result, and perpendicular slope interpretation with domain checks. Download CSV and PDF reports with one click now.

Input
Opposite reciprocal = −1 / m Domain: m ≠ 0 If m is undefined, result is 0
Result
Input Reciprocal (1/m) Opposite Reciprocal (−1/m) As Fraction Notes
Enter a value and press Calculate.

Formula used

m' = -1/m for any real m ≠ 0.

  • If m = 0, the opposite reciprocal is undefined.
  • If m is undefined (vertical line), then m' = 0.
  • For a fraction m = a/b (with b ≠ 0), the opposite reciprocal is m' = −b/a, then simplify.
How to use this calculator
  1. Enter a value: decimal, fraction a/b, mixed a b/c, or undefined.
  2. Optionally adjust decimal precision and the maximum fraction denominator.
  3. Click Calculate to see reciprocal, opposite reciprocal, and fractions.
  4. Read domain notes for zero or undefined special cases.
  5. Export the result table as CSV or PDF using the buttons.
Example data
Input Reciprocal Opposite Reciprocal Opposite Reciprocal (Fraction) Comment
20.5-0.5-1/2Valid, nonzero
-3/4-1.33333333331.33333333334/3a/b → −b/a
0undefinedundefined—Zero is not allowed
undefined000/1Vertical ⟂ horizontal
1.25e-280-80-80/1Scientific notation
Opposite Reciprocal — Quick Reference

Typical inputs and their reciprocals, opposite reciprocals, and domain notes.

Input m Reciprocal 1/m Opposite Reciprocal −1/m Opposite Reciprocal (Fraction) Domain Note
20.5-0.5-1/2Real, nonzero
-1/3-333/1Fraction input
4/51.25-1.25-5/4Fraction input
-7/2-0.28571428570.28571428572/7Improper fraction
0undefinedundefined—Not allowed; vertical perpendicular
undefined000/1Vertical line → horizontal
Perpendicular Slope & Line Examples

From a line with slope m, a perpendicular has slope m' = -1/m (when defined). Through point (x₀, y₀), equation is y - y₀ = m'(x - x₀).

Given Line Slope m Perp. Slope m' Through Point Perpendicular Line
y = 2x + 1 2 -1/2 (3, -2) y = -0.5x - 0.5
y = -(3/4)x + 5 -3/4 4/3 (0, 0) y = 1.3333333333x
y = 4 0 undefined (3, 1) x = 3
x = -2 undefined 0 (3, 1) y = 1
FAQs

It is the negative reciprocal of a number m: compute -1/m, provided m ≠ 0.

If a line has slope m, a perpendicular line has slope -1/m when both slopes are defined and m ≠ 0.

When m=0, -1/m is undefined. This corresponds to a vertical line perpendicular to a horizontal line.

Treat an undefined slope as a vertical line. Its perpendicular slope is 0.

Yes. Use the format a b/c, like 2 1/3. The tool converts it to an improper fraction.

Yes. Decimals and scientific notation are approximated to fractions using continued fractions with a configurable maximum denominator.

No. This tool focuses on real numbers and slopes. Complex arithmetic is outside the current scope.

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