Double Prime Symbol — Definition, Formula & Examples
The double prime symbol (″) is two short vertical strokes written as a superscript after a number or variable. It most commonly denotes inches, arc seconds, or the second derivative of a function.
The double prime (″, Unicode U+2033) is a typographic and mathematical symbol consisting of two prime marks. In measurement, it abbreviates the inch (1″ = 1 inch) and the arc second (1″ = 1/3600 of a degree). In calculus, denotes the second derivative of with respect to .
How It Works
Context determines the meaning of ″. When it follows a number in a measurement, such as , the single prime means feet and the double prime means inches. In angular measure, means 42 degrees, 15 arc minutes, and 30 arc seconds. In calculus, writing is shorthand for , the rate of change of the rate of change.
Worked Example
Problem: A person's height is listed as 5′ 8″. Convert this entirely to inches.
Interpret the symbols: The single prime (′) stands for feet and the double prime (″) stands for inches, so the height is 5 feet and 8 inches.
Convert feet to inches: Multiply the feet value by 12.
Add remaining inches: Combine the two parts.
Answer: 5′ 8″ equals 68 inches.
Why It Matters
You will encounter the double prime symbol whenever you read architectural blueprints, geographic coordinates, or calculus notation. Knowing that the same symbol carries different meanings in different fields prevents costly misreadings in physics, engineering, and navigation problems.
Common Mistakes
Mistake: Using straight quotation marks (") instead of the true double prime symbol (″).
Correction: The quotation mark is a different character. In formal or technical writing, use the proper double prime (″, Unicode U+2033) or, in LaTeX/KaTeX, write with two apostrophes inside math mode.