Basis Point Calculator - Convert BPS to Percent, Permille and Decimal

What is a basis point?

A basis point (often denoted as BP or BPS and pronounced as "bip" or "beep") is a unit of measurement frequently used in finance. It is equal to 1/100th of 1 percent, which is equivalent to one permyriad (1‱). The concepts of percent, permille, permyriad, and basis point are related in the following way:

• 1 percent (1%) = 1/100 = 0.01
• 1 permille (1‰) = 1/1,000 = 0.001
• 1 permyriad (1‱) = 1/10,000 = 0.0001
• 1 basis point (1 BPS) = 0.01% = 0.1‰ = 0.0001 (decimal)

The basis point calculator above uses these equations to help you convert basis points to percents, permilles, and decimal values instantly.

Why do we have basis points?

You may ask yourself why we need basis points if they are the same as permyriads. The relationship between a basis point and a permyriad is similar to the difference between a percent and a percentage point. A basis point equals the value of a permyriad numerically, but it is specifically used when talking about changes in percentage rates.

For example, suppose that in some country the unemployment rate in 2017 was 6%. By 2018, this value had changed to 16%. You may want to say that "the value has increased by 10%," but this is ambiguous — do you mean it changed from 6% to 6.6% (a relative change), or from 6% to 16% (an absolute change)?

To avoid this confusion, you can say it has increased by 1,000 BPS. This makes it clear that you mean the second scenario — an increase in percentage points, not a percentage of a percentage. Basis points help eliminate ambiguity when talking about rate changes in finance.

How to convert basis points to percents?

The easiest way is to put a number into the basis point calculator above and let it do the math for you! However, if you want to do it by hand:

• Basis points → Percent: divide the BPS value by 100.
  Example: 50 BPS ÷ 100 = 0.50%
• Percent → Basis points: multiply the percentage by 100.
  Example: 0.25% × 100 = 25 BPS
• Basis points → Permille: divide by 10.
  Example: 50 BPS ÷ 10 = 5‰
• Basis points → Decimal: divide by 10,000.
  Example: 50 BPS ÷ 10,000 = 0.005

Practical example

You read that "The average rate for a 30-year fixed mortgage is 4.09%, an increase of 9 basis points since last week."

1. Convert BPS to percent: 9 ÷ 100 = 0.09%
2. Subtract from current rate: 4.09% − 0.09% = 4.00%
3. The average rate used to be 4.00%.

Another example: Australia's central bank benchmark interest rate decreased from 1.5% to 1.25%.

1. Find the difference: 1.5% − 1.25% = 0.25%
2. Convert to BPS: 0.25 × 100 = 25
3. The interest rate decreased by 25 BPS.

American vs. metric measurement context

Basis points are a universal financial unit, used identically in both American and international (metric) financial systems:

• American financial system: Basis points appear constantly in U.S. Federal Reserve announcements, mortgage rates, Treasury yield spreads, and corporate bond pricing. When the Fed moves rates by 25 BPS (0.25%), markets react globally.
• International / metric context: The European Central Bank (ECB), the Bank of England, the Bank of Japan, and virtually every central bank worldwide communicates rate changes in basis points. This makes BPS a truly global standard.
• Permille and permyriad (common in metric-oriented scientific and actuarial contexts) map directly: 1 BPS = 0.1‰ = 1‱.

Where are basis points used?

Basis points are mainly used in finance to describe percentage changes and to denote differences between two interest rates, especially when the rate difference is less than 1%. Common use cases include:

• Mortgage loans: Lenders quote rate changes in BPS. If your mortgage is at 3.62% and decreases by 15 BPS, it is now at 3.47%.
• Treasury bonds: The yield spread between 2-year and 10-year Treasuries is measured in BPS.
• Corporate bonds: Credit spreads (the extra yield over government bonds) are quoted in BPS.
• Central bank policy: Rate hikes and cuts are announced in BPS increments (typically 25, 50, or 75 BPS).
• Interest rate derivatives: Swaps, caps, and floors reference BPS for pricing.
• Credit derivatives: Credit default swap (CDS) spreads are quoted in BPS per year.
• Investment funds: Management fees are often expressed in BPS (e.g., "20 BPS annual fee").

While a single basis point may seem tiny, small changes in rates can have very substantial economic outcomes — especially when applied to large principal amounts or across entire economies.

FAQs

How many basis points is 1%?

1% equals exactly 100 basis points (BPS).

What is 1 basis point as a decimal?

1 BPS = 0.0001 as a decimal.

What are basis points in mortgages?

A basis point in a mortgage represents a change equivalent to 0.01%. For example, if your mortgage was at 3.62% and decreases by 15 basis points, it is now at 3.47%.

How do basis points affect investment returns?

On a $100,000 investment, each 1 BPS change in annual return equals $10 per year. Use the Financial Impact section of the calculator above to see the exact dollar impact for any amount and currency.

Is a basis point the same as a pip?

Not exactly. In forex trading, a "pip" is the smallest price movement (0.0001 for most currency pairs), which does equal 1 BPS in percentage terms. However, "pip" and "basis point" are used in different contexts and are not interchangeable terms.