1) Definitions that win featured snippets
Basis points (bps) are a precise way to talk about small movements in rates and spreads. One basis point is one-hundredth of a percent: 1 bp = 0.01% = 0.0001 in decimal. Because finance often deals in small changes (e.g., policy rates, bond yields, credit spreads), quoting moves in bps prevents ambiguity that arises when someone says “up 0.25%.” In basis points, we can say “up 25 bps,” which everyone reads as an absolute +0.25 percentage-point move.
Percentage points (pp) always refer to an absolute difference between two percentages. If a mortgage rate rises from 5% to 7%, the absolute change is +2 percentage points (not +2%). Percentage points don’t depend on the starting value; they’re simply the arithmetic difference of two percentages.
Percent change is a relative change that depends on the starting value. It answers “how much bigger/smaller is the new value relative to the old?” The formula is (new − old) / old × 100%. From 5% to 7%, the relative change is 2/5 = 40%. Percent change equals percentage points only in the special case where the base is 100%.
Example snapshot: 3.00% → 3.25% = +25 bps = +0.25 pp = +8.33% (relative). The bps and pp interpretations are base-independent; the percent-change lens scales with the base.
2) Conversions & formulas (math & spreadsheets)
Math relationships
- Bps → percentage points: pp = bps × 0.01% (i.e., divide by 100)
- Bps → decimal: decimal = bps × 0.0001 (i.e., divide by 10,000)
- Percentage points → bps: bps = pp × 100
- Percent change: %Δ = (new − old) / old × 100%
- % change implied by a bps move (base = r%): %Δ = (bps / r)
Excel & Google Sheets
| Task | Formula | Notes |
|---|---|---|
| bps → % | =A2/10000 | If cell A2 has bps (e.g., 25 → 0.25%) |
| % → bps | =A2*10000 | Format A2 as percent (e.g., 0.25% → 25 bps) |
| Percentage points | =B2 - A2 | Both A2 and B2 are percentages |
| Percent change | =(B2 - A2)/A2 | Format result as percent |
| bps move’s %Δ at base r% | =A2 / r | e.g., 25 bps at 3% base → =25/3 → 8.33% |
3) Master comparison tables
Start with the base-independent conversions: bps ⇄ pp ⇄ % (absolute). Then, show how percent change (relative) depends on the base.
| Basis points | Percentage points | Percent |
|---|---|---|
| 10 bps | 0.10 pp | 0.10% |
| 25 bps | 0.25 pp | 0.25% |
| 50 bps | 0.50 pp | 0.50% |
| 75 bps | 0.75 pp | 0.75% |
| 100 bps | 1.00 pp | 1.00% |
| Base % | 10 bps | 25 bps | 50 bps | 75 bps | 100 bps |
|---|---|---|---|---|---|
| 1% | 10.00% | 25.00% | 50.00% | 75.00% | 100.00% |
| 2% | 5.00% | 12.50% | 25.00% | 37.50% | 50.00% |
| 3% | 3.33% | 8.33% | 16.67% | 25.00% | 33.33% |
| 5% | 2.00% | 5.00% | 10.00% | 15.00% | 20.00% |
| 10% | 1.00% | 2.50% | 5.00% | 7.50% | 10.00% |
Rounding shown to two decimals for readability. For audit-sensitive contexts, state your rounding rule (e.g., banker's rounding) and stick to it consistently.
4) Worked examples (clear, auditable, real-world)
- Central bank hike: 3.00% → 3.25% ⇒ +25 bps, +0.25 pp, +8.33% relative (0.25/3.00).
- Loan APR cut: 7.50% → 7.00% ⇒ −50 bps, −0.50 pp, −6.67% relative (−0.50/7.50).
- Bond spread widens: 120 bps → 155 bps ⇒ +35 bps (= +0.35 pp). Relative change vs base spread is 35/120 = 29.17% if needed.
- Signup rate improves: 5% → 7% ⇒ +2 pp and +40% relative (2/5).
- Churn falls: 4% → 3% ⇒ −1 pp and −25% relative (−1/4).
- Fee disclosure: 0.80% AUM fee increases by 15 bps ⇒ new fee 0.95% (= +0.15 pp). Relative change = 0.15/0.80 = 18.75%.
Why journalists and analysts prefer bps
“Up 0.25%” could be read as up 0.25 percentage points (from 3.00% to 3.25%) or up 0.25 percent (relative) which would be a negligible change. Saying “up 25 bps” eliminates ambiguity and improves comparability across reports.
5) When to use which
- Use basis points when discussing interest rates, bond yields, credit spreads, discount rates, and fee schedules. Precision and shared convention make communication unambiguous.
- Use percentage points when comparing two percentages in absolute terms (conversion rates, unemployment rates, tax rates, churn, CTR).
- Use percent change when you need a relative perspective for KPIs, growth rates, and analytics—particularly when comparing different baselines.
6) Common pitfalls (and how to avoid them)
- Mixing pp with %: “Up 2%” is not the same as “up 2 percentage points.” Prefer pp for absolute changes.
- Reporting bps for counts: Basis points are for rates/spreads. For counts or totals, use %, pp, or absolute numbers.
- Ignoring the base for % change: Relative changes explode when bases are small (e.g., a 10 bps rise at a 1% base is a 10% relative change).
- Over-rounding: State your rounding policy and apply it consistently; keep at least two decimals for small bases.
7) Mini how-to workflow
- Identify the story: Are you describing an absolute move between two percentages (→ pp) or the relative impact vs the starting level (→ % change)?
- Pick the unit: If it’s a rate/spread context (policy, yield, spread), prefer bps; otherwise pp or %.
- Convert carefully: Use the formulas above. Double-check with a spreadsheet and keep consistent rounding.
- Communicate clearly: State both absolute and relative moves when useful (e.g., “+25 bps, or +8.33% relative to 3.0%”).
8) Visuals you can add
Diagram idea: Show old% → new% on a number line. Label the absolute gap as “pp” and the tiny slice as “bps” (where 100 bps = 1 pp). Add a note bubble computing percent change against the base.
Chart idea: Plot the relative % change from a constant 25 bps move against bases from 0.5% to 10%. The curve falls hyperbolically, illustrating why the base matters.
9) SEO assets & internal links
Primary keyword targets
- basis points vs percentage points
- basis points vs percent
- percentage points vs percent change
- bps to percent, bps to pp, 25/50/100 bps meaning
Internal links (update slugs to your site)
- Basis Points (BPS) Explained: 25/50/75/100
- BPS ↔ Percent Converter (calculator)
- APR vs APY vs EAR
- Percent Change Calculator
10) FAQ
How many basis points are in 1 percent?
There are 100 basis points in 1 percent.
Is 25 bps the same as 0.25%?
Yes. 25 basis points equals 0.25%, which is 0.0025 in decimal.
What’s the difference between percentage points and percent change?
Percentage points are absolute differences between two percentages; percent change measures the relative difference versus the starting percentage.
When should I use basis points?
Use basis points for rates, yields, and spreads—contexts where tiny, unambiguous changes matter (policy rates, bond markets, fee schedules).
How do I convert bps to percent?
Divide by 10,000. For example, 50 bps = 0.50%.
11) Editorial checklist
- Put the table above the fold with a “Jump to tables” anchor.
- Use exact numbers (0.25%, not “~0.3%”) and declare your rounding policy.
- Add alt text and captions: “Table converting basis points to percentage points and percent.”
- Include worked examples for 25/50/75/100 bps at 3% and 5% bases.
- Reinforce the core idea: bps & pp are base-independent; % change is base-dependent.
- Link to your related articles and calculators to improve dwell time and topical coverage.