ExactUnits
↑↓ move ↵ open Esc close All shortcuts

Golden ratio calculator

The golden ratio is the only positive number that is one more than its own reciprocal.

Longer part
61.803 398 875
≈ Rounded Golden ratio
Shorter part
38.196 601 125
Ratio of the parts
1.618 033 988 749 894 848 2
Length extended by the ratio
161.803 398 875
Show the working
  1. Total length = 100
  2. Longer part = 100 / phi = 61.8034
  3. Shorter part = 100 - 61.8034 = 38.1966
  4. Ratio of the parts = 38.1966 > 0 ? 61.8034 / 38.1966 : 0 = 1.618 03
  5. Length extended by the ratio = 100 * phi = 161.803

Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.

Scenarios & local history

Compare a saved scenario

Recent calculations

    The formula

    • phi = (1 + sqrt 5) / 2 = 1.6180339887...
    • phi = 1 + 1/phi

    Related calculators

    Settings

    Theme

    System follows your operating system and changes with it.

    Text size
    High contrast

    Maximises text and border contrast and removes the grid background.

    Graph-paper background
    Round to
    Notation
    Thousands separators
    Decimal mark
    Nearest fraction

    Shows the result as the nearest tape-measure fraction, with the error it costs.

    Accessibility & interaction
    Reduce motion Stops interface animations even when the operating system does not.
    Underline links Keeps links visually distinct without relying on colour.
    Larger touch targets Makes buttons and form controls easier to tap.
    Shorter reading lines Limits article width for easier scanning.
    Monochrome display Removes colour as an information cue.
    Always-visible focus Makes the keyboard focus ring persistent and stronger.
    Verbose screen-reader results Announces the complete conversion equation.
    Sticky action bars Keeps converter and calculator actions within reach.
    Select values on focus Replaces a value immediately when you start typing.
    Left-handed mobile layout Moves key mobile actions toward the left thumb.
    Your data

    Settings, recent conversions and favourites live in this browser only. Nothing is sent anywhere.

    Offline library