Golden Ratio Calculator

The golden ratio is a special proportion represented by the Greek letter phi. Its value is approximately 1.6180339887. Two positive segments are in the golden ratio when the longer segment divided by the shorter segment equals the total length divided by the longer segment. This calculator finds all three measurements from any one known measurement, preserving that relationship with full calculation precision. If the shorter segment is known, multiply it by phi to obtain the longer segment. Add those two lengths, or multiply the shorter segment by phi squared, to find the total. If the longer segment is known, divide it by phi for the shorter segment and multiply it by phi for the total. If the complete length is known, divide by phi for the longer part and divide by phi squared for the shorter part. Each route describes the same proportion. The golden ratio appears in geometry through the golden rectangle, golden spiral, pentagon, and pentagram. Designers may use it as one possible guide for dividing page layouts, images, typography, furniture, or architectural features. Artists sometimes place an important boundary or focal region near a golden section. These uses are compositional choices rather than guarantees of beauty, but the ratio supplies a consistent proportional framework that is easy to scale. Phi also has a close relationship with the Fibonacci sequence. Ratios of consecutive Fibonacci numbers approach phi as the sequence progresses, although no finite pair equals the irrational number exactly. Algebraically, phi is the positive solution of a quadratic equation in which the square of the number equals the number plus one. That identity explains why multiplying or dividing adjacent golden-ratio lengths produces such neat relationships. All three calculator outputs use the same unit as the entered value. Enter centimeters to receive centimeters, pixels to receive pixels, or any other consistent length unit. The result is rounded for display, so adding the displayed shorter and longer values can occasionally differ from the displayed total in the last decimal place. The internal values maintain greater precision. Use the calculated dimensions as practical measurements, and round them only as much as your design, craft, or construction process requires.