How To Find Percentage Of A Number Between Two Numbers

You're staring at two numbers — maybe a starting salary and a target salary, or last month's revenue versus this month's — and you need to know where a third number sits between them. So as a percentage. It sounds like middle-school math until you actually have to do it in a spreadsheet at 6 PM on a Friday.

Here's the thing: most people overcomplicate this. They reach for online calculators or nested IF formulas when the logic is actually straightforward once you see it visually.

What Is Percentage Between Two Numbers

When someone asks "what percentage is X between A and B," they're usually asking one of two different questions — and confusing them is where the trouble starts.

The position question

This is interpolation. Even so, you have a range: minimum value A, maximum value B. You have a value X that falls somewhere between them. You want to know: if A is 0% and B is 100%, what percentage is X?

Think of a thermometer. Day to day, freezing is 0°C, boiling is 100°C. If the mercury sits at 37°C, it's at 37% of the way from freezing to boiling. That's the position question.

The proportion question

This is simpler. You have two numbers. You want to know what percentage one is of the other. "What percent of 80 is 20?Also, " Answer: 25%. This isn't about a range — it's about a part-to-whole relationship.

Both use division. Both multiply by 100. But the denominator changes. That's the whole trick.

Why It Matters

You hit this constantly without labeling it "percentage between two numbers."

Salary negotiations: the offer is $72,000. Which means where does $72K land as a percentage of your acceptable range? The minimum you'd accept is $65,000. Because of that, you wanted $85,000. That number changes how you feel about the offer — and how you counter.

Fitness tracking: your resting heart rate is 58. Also, your max (estimated) is 182. What percentage of your heart rate reserve is that? Day to day, during a workout you hit 142. That's zone training, and the formula is exactly the position question above.

Budget variance: projected spend $40K, actual $52K, cap $60K. Practically speaking, you're not just over budget — you're 80% of the way from projection to disaster. That framing gets attention in a way raw numbers don't.

Grading curves: the highest score is 94, lowest is 52, a student got 78. Worth adding: where do they sit? That's a percentage-between calculation every teacher runs (or should run) before curving.

The pattern: any time you have a floor, a ceiling, and a current value, you're doing this math. Naming it lets you automate it, explain it, and stop guessing.

How It Works

Let's derive both versions from scratch so you never have to memorize a formula again.

Position percentage (interpolation)

You have:

Low = L (the floor, 0%)
High = H (the ceiling, 100%)
Value = V (the number somewhere between)

The distance from floor to ceiling is H − L. The distance from floor to your value is V − L.

The fraction of the way you've traveled: (V − L) / (H − L)

Multiply by 100 for percentage: ((V − L) / (H − L)) × 100

That's it. That's the entire formula.

Let's test it. Consider this: distance from floor = 100. Consider this: 100/200 = 0. L = 200, H = 400, V = 300. Because of that, 5. Still, × 100 = 50%. Range = 200. Makes sense — 300 is exactly halfway between 200 and 400.

Another: L = 50, H = 150, V = 50. Range = 100. Also, distance = 0. 0/100 = 0%. The value is the floor.

One more: L = 50, H = 150, V = 150. So naturally, range = 100. Consider this: distance = 100. 100/100 = 1. × 100 = 100%. The value is the ceiling.

What if V is outside the range? Now, say V = 175. Because of that, distance = 125. On the flip side, 125/100 = 1. 25. Practically speaking, × 100 = 125%. The formula still works — it just tells you you're 25% past the ceiling. Negative percentages mean you're below the floor. This is useful for flagging outliers automatically.

Proportion percentage (part of whole)

You have:

Whole = W
Part = P

Percentage = (P / W) × 100

That's the one everyone learns in school. "What percent of 80 is 20?" → (20/80) × 100 = 25%.

The trap: people use this formula when they should use the interpolation formula. If your salary range is $60K–$100K and the offer is $80K, the proportion formula gives you (80,000 / 100,000) × 100 = 80%. But that's meaningless — the floor isn't $0. Plus, the interpolation formula gives ((80,000 − 60,000) / (100,000 − 60,000)) × 100 = 50%. That's the real answer.

Percentage change (a third variant)

Sometimes "between two numbers" means change over time. Old value O, new value N.

((N − O) / |O|) × 100

The absolute value on the denominator handles negative starting values. If revenue went from −$10K (a loss) to $20K (profit), the change is (30,000 / 10,000) × 100 = 300% improvement. The formula holds.

But this isn't "percentage between" — it's "percentage change from." Different question. Different denominator.

Doing it in Excel / Google Sheets

Position percentage:

=(V - L) / (H - L)

Format the cell as percentage. Done.

Proportion:

For more on this topic, read our article on how many days till august 12 or check out how many days until september 3.

=P / W

Format as percentage.

Percentage change:

=(N - O) / ABS(O)

Format as percentage.

Pro tip: name your cells. Still, " Select V, type "Value. " Now your formula reads =(Value - Floor) / (Ceiling - Floor). That said, select L, type "Floor" in the name box. Plus, select H, type "Ceiling. Six months from now you'll still understand it.

Doing

Doing it in other tools

If you prefer a scriptable approach, the same arithmetic works in virtually every language.

Python (pandas)

import pandas as pd

df = pd.DataFrame({
    "Floor": [200, 50, 50],
    "Ceiling": [400, 150, 150],
    "Value": [300, 50, 150]
})

# Position percentage (0‑100 %)
df["Position%"] = (df["Value"] - df["Floor"]) / (df["Ceiling"] - df["Floor"]) * 100

df <- data.frame(
  Floor = c(200, 50, 50),
  Ceiling = c(400, 150, 150),
  Value = c(300, 50, 150)
)

df$PositionPct <- (df$Value - df$Floor) / (df$Ceiling - df$Floor) * 100

SQL (PostgreSQL syntax)

SELECT
  (value - floor) * 100.0 / (ceiling - floor) AS position_pct
FROM compensation;

All of these will give you the same 0‑100 % scale, and they can be chained with CASE statements to flag outliers automatically, e.g.:

, CASE
    WHEN (value - floor) * 100.0 / (ceiling - floor) > 100 THEN 'Above ceiling'
    WHEN (value - floor) * 100.0 / (ceiling - floor) < 0  THEN 'Below floor'
    ELSE 'Within range'
  END AS status

Common pitfalls & how to avoid them

Pitfall	Why it hurts	Fix
Using proportion when you need interpolation	The denominator should be the range* (`H‑L`), not the absolute whole (`W`).	Always ask: “Is there a meaningful floor?” If the floor isn’t zero, use the interpolation formula. Consider this:
Ignoring division‑by‑zero	If `H == L` the range collapses; the formula blows up.	Guard with `IF(H=L, NA(), (V‑L)/(H‑L)*100)`.
Negative ranges	When `H < L` (e.g., a decreasing scale) the sign flips. And	Use `ABS(H‑L)` in the denominator if you want a non‑negative percentage, or keep the sign to preserve direction.
Absolute vs. Because of that, relative change	Mixing up “percentage of whole” with “percentage change” leads to wrong business stories.	Clarify the question: What portion of the range?* → interpolation. Now, how much did it move from the start? * → percentage‑change formula.
Formatting quirks	Excel treats `0.5` as 50 % only after applying percentage formatting; raw numbers can be misread.	Apply the format before inspecting the cell, and consider adding a `%` suffix in headers for clarity.

When to reach for each formula

Situation	Recommended formula	Example
Salary band analysis – you have a defined minimum (`L`) and maximum (`H`).	Interpolation: `(V‑L)/(H‑L)×100`	Offer $80K in a $60K‑$100K band → 50 % position.
Market‑share reporting – “What percent of total market does this segment own?”	Proportion: `P/W×100`	Segment sales $25M of $100M total → 25 %.
Year‑over‑year growth – you want to know how much the metric changed relative to its starting point. So naturally,	Percentage change: `(N‑O)/	O
Performance scoring – you map raw scores onto a 0‑100 scale with a floor and ceiling.	Interpolation (same as salary band).	Test score 72 in a 60‑90 range → 20 % above floor.

Quick reference cheat‑sheet

Goal	Formula	Excel / Sheets	Python (pandas)	R
Position within a bounded range	`(V‑L)/(H‑L)×100`	`=(V-L)/(H-L)` (format % )	`(df['V']-df['L'])/(df['H']-df['L'])*100`	`(df$Value - df$Floor) / (df$Ceiling - df

Summary: Choosing the Right Tool

Mastering these formulas is less about memorizing the syntax and more about understanding the context of the data. Before you type a single character into your spreadsheet or script, pause to identify three critical components:

The Baseline (The "Zero"): Are you measuring from a fixed zero, or is there a meaningful floor (like a minimum salary or a minimum test score)?
The Boundary (The "Whole"): Are you comparing a part to a total, or a value to a specific range?
The Intent: Are you trying to show magnitude (how big something is) or position (where something sits)?

If you treat every percentage as a simple "part-to-whole" calculation, you will inevitably misrepresent your data—reporting a salary as "50% of the total" when it is actually "50% of the range." By applying the correct mathematical model—whether it be proportion, interpolation, or percentage change—you see to it that your insights are not just mathematically accurate, but contextually meaningful.

In the world of data analysis, a percentage is only as good as the logic used to derive it. Use these formulas wisely, guard against division-by-zero, and always double-check your boundaries.