The math

Headroom: staying under your target proof

2 minute read · The Blending School

Headroom answers the practical question the basic formula does not: not 'what will the proof be' but 'how much can I add before I cross my line.'

The question

Your bottle holds 20 ounces at 106.7. You like it under 110, and you are holding a 124.9 proof Booker's. How much can go in? Guessing means overshooting. The algebra means knowing.

The derivation

Set the blend formula equal to the target T and solve for the incoming volume x, with bottle volume V at proof P, incoming proof p:

Worked

You can add 4.4 ounces of Booker's before the bottle crosses 110. Pour 2 and you have banked the rest for next time.

Reading the edge cases

• Incoming proof below target: the formula flips into a floor calculation: how much soft whiskey before you sink below a minimum. Same algebra, opposite worry.
• Incoming proof equals target: the denominator hits zero, which is the math saying the answer is "infinite": whiskey at exactly your target can never push you past it.
• Already past the target: the result goes negative, meaning no amount of this pour helps; the fix is water or a softer whiskey.

Headroom is the single most useful number to know at the moment of pouring, and almost nobody computes it by hand at 9 pm with a bottle in the other hand. It is exactly the kind of arithmetic an app should be doing live, which is why Thief & Blend prints the headroom line right on the pour screen.