Conversion Formulas and Relationships
The calculator converts between four proportional units using these core relationships:
decimal = basis points / 10,000
percent = basis points / 100
permille = basis points / 10
dollar impact = decimal x position size
For example, entering 50 basis points produces: 0.00500000 decimal, 0.50%, 5.0000 permille, and $5,000.00 on a $1,000,000 position.
Every conversion is a rearrangement of the same relationship -- if you start with percent, the calculator multiplies by 100 to get basis points, then derives everything else.
Example: 50 Basis Points on a $1,000,000 Position
Here is the step-by-step math for the default example:
- Basis points to percent: 50 / 100 = 0.50%
- Basis points to decimal: 50 / 10,000 = 0.00500000
- Basis points to permille: 50 / 10 = 5.0000‰
- Dollar impact: 0.005 x $1,000,000 = $5,000.00
The reference table extends this to common values:
| Basis Points | Percent | Decimal | Dollar Impact |
|---|---|---|---|
| 1 | 0.01% | 0.0001 | $100 |
| 25 | 0.25% | 0.0025 | $2,500 |
| 50 | 0.50% | 0.0050 | $5,000 |
| 100 | 1.00% | 0.0100 | $10,000 |
| 200 | 2.00% | 0.0200 | $20,000 |
| 500 | 5.00% | 0.0500 | $50,000 |
When to Use Each Unit
Basis points are standard in finance for interest rate changes, bond yields, credit spreads, and fund fees.
A Fed rate move of 25 bps ($2,500 per $1,000,000) is clearer than saying "a quarter of a percent."
Percent is the most widely understood format for general audiences.
Use it in client-facing reports and everyday comparisons.
Permille appears in specialized fields like insurance pricing and scientific measurements. 50 bps = 5.0‰.
Decimal is needed when plugging rates into spreadsheet formulas or financial models. 50 bps = 0.0050 as a multiplier.