Reverse-Engineering My Weight Gain

Most calorie calculators look forward: How much should I eat now?

I wanted to look backward to see where I went wrong.

From my wedding in November 2019 to my heaviest weight in April 2022, I went from 180 lb (81.6 kg) to about 215 lb (97.5 kg) — during COVID lockdowns, daily drinking, disrupted and inconsistent training, and the first months of parenthood.

Instead of guessing what went wrong, I asked a different question: "Given my height, estimated body fat, activity level, and time span — and assuming relatively even eating habits — how many extra calories per day would explain this weight gain?"

With the help of math (*ahem*, ChatGPT — I'm terrible at math), I built a backward-looking energy balance model.

The result surprised me: we weren't talking about a big surplus... but, rather, about 135–155kcal per day over about two and a half years.

Step 1: Define a reference body mass from body-fat targets

Rather than using BMI, I defined an “expected” body mass based on body composition.

Let:

• m = body mass at my heaviest (kg)

• BF = estimated body fat fraction at that time

• BF* = target body fat fraction

• FFM = m(1-BF) = fat-free mass

• mref = FFM/(1-BF*) = reference body mass

Using my (estimated) data (I didn't start tracking my metrics well until more recently):

• m = 97.5 kg

• BF ≈ 0.26–0.28 (estimated)

• BF* = 0.12 (target)

This yields a reference mass between:

mref ≈ 79.9–82kg (≈ 176–181lb)

So relative to a healthy body-fat target, I carried about:

Δm ≈ 15.5–17.7kg of excess mass.

Step 2: Convert excess mass into stored energy

Assume a long-term energy equivalent of mass change:

⍺ ≈ 7700 kcal·kg^(-1)

A more detailed formulation to replace the single constant ⍺ with a composition-weighted energy density:

p = fraction of mass gain as fat

⍺f ≈ 9500 kcal/kg (fat tissue)

⍺ℓ ≈ 2000 kcal/kg (lean tissue)

⍺eff = p⍺f + (1-p)⍺ℓ 

Estore = ⍺eff(m-mref)

For clarity, this post uses ⍺ ≈ 7700 kcal/kg as a commonly accepted long-term approximation.

Stored energy:

Estore = ⍺Δm

Estore ≈ 119,000–136,000kcal

Step 3: Spread that surplus across time

Let:

• t = 882 days (Nov 2019 → Apr 2022)

• ΔĒ = mean daily energy surplus

ΔĒ = Estore/t

ΔĒ ≈ 135–155kcal/day

This gives the mean daily energy surplus required to produce the observed excess mass over the specified time window. To relate this surplus to eating behavior, define the implied mean intake:

Ī = TDEEref + ΔĒ 

where TDEEref is the estimated maintenance energy expenditure at the reference body mass.

The implied mean intake (Ī) presents the average daily caloric intake that would be required to generate the observed mass gain over the time period considered.

Simply put: once the surplus is known, adding it to maintenance calories tells you roughly how much you must have been eating, on average.

That's it: about 145 kcal per day, on average.

Sustained quietly over two and a half years.

What that actually means

One hundred forty-five calories is:

• one bottle of beer

• half a bagel

• a chocolate chip cookie or like three Oreos

• 3/4 cup of cooked white rice

• a Jack and Coke

That's not bingeing. It's hard to even consider it problematic eating; it's more of a rounding error: a small surplus over a long time.

Which explains why weight gain feels mysterious. And why fat loss feels hard.

It isn’t dramatic; it’s cumulative.

How this reframes everything

This model removes shame and replaces it with math:

• Weight gain is not a character flaw

• It’s energy balance integrated over time

• And it’s reversible using the same equation

If +145 kcal/day built it, then -145 kcal/day can undo it.

Same equation; different sign.

Assumptions

This model assumes:

• a roughly constant average surplus over time

• stable activity patterns

• a simplified energy density of mass change

• no attempt to dynamically model metabolic adaptation

It is not a physiological simulator — it is a conceptual and educational model.