Enter an angle and a side, or two known sides, and this calculator identifies which SOH-CAH-TOA ratio applies and solves the rest.
How to Use the SOHCAHTOA Calculator
In Find a Side mode, enter an acute angle and pick which side is already known — Opposite, Adjacent, or Hypotenuse. In Find the Angle mode, pick which two sides are known instead, and it solves for the angle between them. Either way, the calculator names the exact ratio it used.
SOHCAHTOA is a mnemonic for the three basic trig ratios in a right triangle, each pairing two sides relative to a chosen angle:
SOH: sin(θ) = Opposite ÷ Hypotenuse
CAH: cos(θ) = Adjacent ÷ Hypotenuse
TOA: tan(θ) = Opposite ÷ AdjacentPicking the right one is mostly a matter of matching what's already known to what's on offer — know the angle and the hypotenuse but need the opposite side, and only SOH involves both, so that's the one to rearrange.
Working Backward to the Angle
The same three ratios invert to solve for the angle once two sides are known, swapping in an inverse trig function for whichever ratio fits: θ = sin⁻¹(O÷H), θ = cos⁻¹(A÷H), or θ = tan⁻¹(O÷A). Which one applies depends entirely on which pair of sides got measured — a surveyor with a height and a ground distance reaches for TOA; someone reading off a rope's length and a wall height reaches for SOH.