Sum and difference calculator (sin)

Reviewed by the CalculatorHub team, edited by James Graham. Method from NIST DLMF (trigonometric functions). Last verified 2026-07-09.

The Sum and difference calculator (sin) computes sum and difference from the relation sin(a+b) = sin a cos b + cos a sin b. It takes 2 inputs (angle a in deg, angle b in deg) and returns the sin(a+b). These calculators serve students working through a trigonometry, surveying or physics course, along with drafters, machinists, carpenters, roofers and navigators who need a function value evaluated quickly, or who need an angle, a side length or a height that cannot be measured directly and has to be recovered from the parts of the figure that can be measured. Enter your values below and the result updates instantly, and you can share a permalink that pre-fills the exact calculation. Where a tool takes or returns an angle, confirm which unit you are working in before you rely on the result, because a value entered or read as degrees when it is meant as radians or gradians changes the answer without any warning, and carry more digits through intermediate values than you plan to report so that rounding does not compound across a multi-step solution. For example, with angle a = 30 deg, angle b = 60 deg, the sin(a+b) works out to 1, and the worked example further down the page shows every step so you can follow the arithmetic and reproduce it by hand. The method is the standard form documented by NIST DLMF (trigonometric functions), and the figure above each result carries the date it was last verified. The relationships themselves hold exactly, but the figure displayed is a rounded decimal standing in for a value that is often irrational, and each function carries its own domain and range limits: the tangent is undefined wherever the cosine is zero, and an inverse function returns only the principal angle, so a triangle solved from two sides and a non-included angle can have a second valid solution that a single result will not show.