1 BPS = 0.01% = 1/10,000
1% = 100 BPS = 1/100
1‰ = 10 BPS = 1/1,000
Decimal representation
Calculate the actual value change when a rate changes by a certain number of basis points.
A basis point (often abbreviated as BPS or bp, and pronounced "bip" or "beep") is a unit of measurement used in finance to describe percentage changes in financial instruments.
🎯 Key Definition:
1 basis point = 0.01% = 1/100 of 1%
This means:
| Unit | Fraction | Decimal | In Basis Points |
|---|---|---|---|
| Percent (%) | 1/100 | 0.01 | 100 BPS |
| Permille (‰) | 1/1,000 | 0.001 | 10 BPS |
| Basis Point (bp) | 1/10,000 | 0.0001 | 1 BPS |
Basis points eliminate ambiguity when discussing percentage changes. They help distinguish between absolute and relative changes.
Example of Ambiguity:
Say a mortgage rate is 5% and it "increases by 10%."
Using Basis Points:
If we say the rate "increased by 100 basis points," it's completely clear:
Learn more about percentage calculations in our Percentage Calculator guide.
Percent = BPS ÷ 100
Example: 250 BPS = 250 ÷ 100 = 2.5%
BPS = Percent × 100
Example: 3.75% = 3.75 × 100 = 375 BPS
Decimal = BPS ÷ 10,000
Example: 150 BPS = 150 ÷ 10,000 = 0.015
BPS = Decimal × 10,000
Example: 0.0225 = 0.0225 × 10,000 = 225 BPS
Scenario: "The average rate for a 30-year fixed mortgage is 4.25%, an increase of 15 basis points since last week."
Solution:
Step 1: Convert BPS to percent
15 BPS ÷ 100 = 0.15%
Step 2: Find the previous rate
4.25% - 0.15% = 4.10%
The rate was 4.10% last week.
Scenario: The Federal Reserve cuts interest rates from 2.25% to 2.00%.
Solution:
Step 1: Calculate the difference
2.25% - 2.00% = 0.25%
Step 2: Convert to BPS
0.25% × 100 = 25 BPS
The Fed cut rates by 25 basis points.
Scenario: You sell a stock option for $150,000 and earn a 30 BPS commission.
Solution:
Step 1: Convert BPS to decimal
30 BPS ÷ 10,000 = 0.003
Step 2: Calculate commission
$150,000 × 0.003 = $450
You earn $450 in commission.
Scenario: A 10-year Treasury bond yield increases by 50 basis points on a $1,000,000 investment.
Solution:
Step 1: Convert BPS to decimal
50 BPS ÷ 10,000 = 0.005
Step 2: Calculate value change
$1,000,000 × 0.005 = $5,000
The yield increase represents $5,000 more in annual interest.
Basis points are commonly used in various financial contexts:
💡 Why So Common?
Basis points are particularly useful when dealing with small rate changes (less than 1%). They provide precision without using awkward decimal places.
For more on investment calculations, see our Simple Interest Calculator and CAGR Calculator.
Quick reference for frequently used basis point conversions:
| Basis Points | Percent | Decimal | Common Usage |
|---|---|---|---|
| 1 BPS | 0.01% | 0.0001 | Smallest unit |
| 5 BPS | 0.05% | 0.0005 | Minor adjustments |
| 10 BPS | 0.10% | 0.001 | Small rate changes |
| 25 BPS | 0.25% | 0.0025 | Quarter point (Fed moves) |
| 50 BPS | 0.50% | 0.005 | Half point |
| 75 BPS | 0.75% | 0.0075 | Three-quarter point |
| 100 BPS | 1.00% | 0.01 | Full percentage point |
| 200 BPS | 2.00% | 0.02 | Two percentage points |
| 500 BPS | 5.00% | 0.05 | Major rate changes |
| 1000 BPS | 10.00% | 0.10 | Ten percentage points |
50 basis points equals 0.5% or 0.005 in decimal form. For example, if an interest rate increases from 3% to 3.5%, that's a 50 basis point increase.
Yes, basis points can be negative when describing decreases. However, it's more common to say "decreased by 25 basis points" rather than "increased by -25 basis points," even though both mean the same thing.
In mortgages, a basis point represents a change of 0.01% in the interest rate. For example, if your mortgage rate was 3.62% and decreases by 15 basis points, your new rate would be 3.47%.
100 basis points equals exactly 1%. This is why basis points are sometimes called "percentage points" - 100 BPS = 1 percentage point.
Basis points eliminate confusion when discussing rate changes. Saying "increased by 10%" is ambiguous (10% of what?), but "increased by 100 basis points" is crystal clear - it means a 1% absolute increase.
To calculate 40 BPS of any amount: