Basis Point Calculator
Enter a decimal, such as 0.0125, to see it in basis points, percent and permille.
Updated
Basis Point Calculator
Our Basis Point Calculator converts a decimal into basis points, percent and permille at the same time. Type a rate, spread, fee or change as a decimal, such as 0.0125, and the three values appear at once with the working. Basis points are the standard unit for interest rate moves, bond spreads and fund fees, because "25 bps" can only mean one thing.
Quick answer
One basis point (bp) is 0.01%, or 0.0001 as a decimal. Basis points = decimal × 10,000: 0.0125 × 10,000 = 125 bps = 1.25%.
- 100 bps = 1%: and 1 bp = 0.01%.
- Percent to bps: multiply the percent by 100, so 0.25% is 25 bps.
- bps to percent: divide by 100, so 75 bps is 0.75%.
- Permille: 1‰ = 0.1% = 10 bps.
What Is a Basis Point?
A basis point is one hundredth of one percent. Traders, banks and fund managers use it to quote small rates and small changes without decimals or doubt. It is written bp, bps or "bips", and it is always an absolute amount: a move from 4.50% to 4.75% is 25 bps.
| Basis points | Percent |
|---|---|
| 1 bp | 0.01% |
| 10 bps | 0.1% |
| 25 bps | 0.25% |
| 50 bps | 0.5% |
| 100 bps | 1% |
| 10,000 bps | 100% |
How to Convert Between Decimals, Percent and Basis Points
Every conversion is a multiplication or a division by a power of 10:
Percent = decimal × 100
Permille = decimal × 1,000
bps = percent × 100
A loan rate of 0.0125 written as a decimal:
- Basis points: 0.0125 × 10,000 = 125 bps.
- Percent: 0.0125 × 100 = 1.25%.
- Permille: 0.0125 × 1,000 = 12.5‰.
To go back, divide: 125 bps ÷ 10,000 = 0.0125. To enter a percent in the calculator, divide it by 100 first, so 1.25% is typed as 0.0125.
Basis Point Examples
| Decimal | Basis points |
|---|---|
| 0.0001 | 1 bp (0.01%) |
| 0.0025 | 25 bps (0.25%) |
| 0.045 | 450 bps (4.5%) |
| 1.5 | 15,000 bps (150%) |
| −0.005 | −50 bps (−0.5%) |
A negative value is a fall: a central bank that cuts its rate from 5% to 4.5% has cut by 50 bps, entered as −0.005. Values above 1 are fine too: a 150% return is 15,000 bps.
Basis Points vs Percent Change
"The rate rose 1%" is ambiguous. If a rate goes from 4% to 5%:
- In basis points it rose 100 bps, or 1 percentage point.
- As a percent change it rose 25%, because 1 ÷ 4 = 0.25.
Basis points always describe the first meaning, the absolute gap between two rates, so they remove the doubt. That is why rate decisions, mortgage quotes and bond spreads are given in bps.
Where Basis Points Are Used
- Policy rates: central banks usually move rates in steps of 25 bps.
- Bond spreads: a corporate bond yielding 4.75% against a 4.50% government bond has a spread of 25 bps.
- Fund fees: an expense ratio of 0.75% is 75 bps, which costs 1,875 a year on 250,000.
- Loans: a mortgage priced at "base rate plus 150 bps" is the base rate plus 1.5%.
The "Of 1,000,000" row shows what the value is worth on a balance of one million. 10 bps on 1,000,000 is 1,000, which is why small differences in basis points matter on large sums.
Key Terms
- Basis point
- 0.01%, or 0.0001.
- bps
- Short for basis points.
- Permille (‰)
- One thousandth: 0.1% or 10 bps.
- Percentage point
- Absolute gap between two percents.
- Spread
- Yield gap, quoted in bps.
How to Use the Basis Point Calculator
- Enter the decimal value. Type the rate, fee or change as a decimal, such as 0.0125 for 1.25%. Negative values and values above 1 work too.
- Read the basis points. The value in basis points appears as you type, with the working, the percent, the permille and the amount on 1,000,000.
- Copy or clear. Press Copy to copy the basis points, or Clear or Esc to start again.
Example: a decimal of 0.045 is 0.045 × 10,000 = 450 bps, which is 4.5% or 45‰.
Who Can Use This Calculator?
Frequently Asked Questions (FAQs)
What is a basis point?
A basis point is one hundredth of one percent: 1 bp = 0.01% = 0.0001. 100 basis points make 1%.
How do you convert a decimal to basis points?
Multiply the decimal by 10,000. For example, 0.0125 × 10,000 = 125 bps.
How many basis points are in 1%?
100. So 0.5% is 50 bps and 2% is 200 bps.
What does a 25 basis point rate hike mean?
The rate rises by 0.25 percentage points, for example from 4.50% to 4.75%.
How do you convert basis points to a percent?
Divide by 100. 75 bps ÷ 100 = 0.75%.
What is the difference between permille and basis points?
Permille is one thousandth (0.1%), and a basis point is one ten-thousandth (0.01%). So 1‰ = 10 bps.
Can basis points be negative or above 10,000?
Yes. A fall is negative, such as −50 bps for a half-point cut, and values above 100% are above 10,000 bps, such as 15,000 bps for 150%.
Is the Basis Point Calculator free?
Yes. It is completely free, needs no sign-up, and can be used as many times as you like.
Sources
- Corporate Finance Institute. Basis Points (BPS).
- Wikipedia. Basis point.
- Wikipedia. Percentage point.
- Wikipedia. Per mille.
- Federal Reserve. Open Market Operations.
- Wikipedia. Expense ratio.
Use our Basis Point Calculator to convert any decimal into basis points, percent and permille in seconds.