Why Percentage, Not Pounds
Twenty pounds lost means something very different at 150 lb than at 350 lb. Percentage of starting weight normalises for that, which is why clinical literature reports it and why weight-loss competitions score on it.
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percentage lost = (starting weight − current weight) ÷ starting weight × 100
`
| Starting | Current | Lost | Percentage |
|---|---|---|---|
| 150 lb | 140 lb | 10 lb | 6.7% |
| 200 lb | 190 lb | 10 lb | 5.0% |
| 250 lb | 240 lb | 10 lb | 4.0% |
| 300 lb | 285 lb | 15 lb | 5.0% |
The Clinically Meaningful Thresholds
These are the figures the research actually reports outcomes against:
| Loss | Documented effect |
|---|---|
| 3–5% | Measurable improvement in triglycerides and blood glucose |
| 5–10% | Blood pressure and cholesterol improve; type 2 diabetes risk falls substantially |
| 10%+ | Sleep apnoea improves; joint pain reduces; the largest metabolic benefit |
Five percent is the number to know. It is small enough to be reachable and large enough that
the health effects are documented rather than theoretical — for a 200 lb person that is 10 lb,
not the 50 lb that a goal weight often implies.Rate Matters More Than Total
A sustainable rate is roughly 0.5–1% of body weight per week. Faster than that increasingly
comes from lean mass and water rather than fat, and is associated with worse maintenance.
| Body weight | Sustainable weekly loss |
|---|---|
| 150 lb | 0.75–1.5 lb |
| 200 lb | 1–2 lb |
| 250 lb | 1.25–2.5 lb |
| 300 lb | 1.5–3 lb |
Weight Is Not Fat
Daily fluctuations of 2–5 lb are normal and are water, glycogen and gut contents rather than
tissue. A single weigh-in is noise; a seven-day moving average is signal. Weigh at the same
time under the same conditions, and judge by the trend line rather than by any one morning.
Body composition matters more than the scale. Someone who loses 10 lb of fat and gains 5 lb
of muscle shows 2.5% on the scale and a much larger change in reality.
*This calculator is arithmetic, not medical advice. Talk to a clinician before starting any
significant weight-loss programme.*
The Four Percentage Questions
Almost every percentage problem is one of these, and mixing them up is the most common
arithmetic error there is:
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | Y × (X ÷ 100) | 15% of 80 = 12 |
| X is what % of Y? | (X ÷ Y) × 100 | 12 is 15% of 80 |
| X is Y% of what? | X ÷ (Y ÷ 100) | 12 is 15% of 80 |
| % change from X to Y | ((Y − X) ÷ X) × 100 | 80 → 92 is +15% |
Percentage Points Are Not Percent
A rate moving from 4% to 5% is one percentage point, and a 25% increase. Both
statements are true and they are not interchangeable — headlines routinely use the smaller
one when reporting a rise and the larger one when reporting a fall.
Increases and Decreases Do Not Cancel
| Start | Change | Result |
|---|---|---|
| 100 | +50%, then −50% | 75 |
| 100 | −50%, then +50% | 75 |
| 100 | −20%, then +25% | 100 |
The reason is that the second percentage applies to a different base. To reverse a −20% you
need +25%, not +20%. This is why a stock that falls 50% must double to break even, and why
"we cut costs 30% then grew 30%" leaves you 9% down.Reversing a Percentage
To find the price before a 20% discount, divide by 0.8 — do not add 20%:
`
before = after ÷ (1 − discount)
$80 ÷ 0.8 = $100 ✓
$80 × 1.2 = $96 ✗
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The same asymmetry applies to tax, tips, markups and platform fees.