Basis Point Calculator

What a basis point is

A basis point is one hundredth of a percentage point. Written as a decimal it is 0.0001, and written in parts per million it is 100. The SEC's Investor.gov glossary defines it in one line: one one-hundredth (.01) of a percentage point, so eight percent is 800 basis points.

That tiny unit exists for a practical reason. When a rate moves from 6.50 percent to 6.75 percent, saying it rose by a quarter of a percent invites an argument. Did it rise by 0.25 percentage points, or by 0.25 percent of 6.50, which is a move to 6.516 percent? Both readings are defensible in plain English. Saying it rose 25 basis points is not open to either reading. Traders shorten the term to bips, and the written forms bp and bps are everywhere in rate sheets.

The arithmetic is simple enough to do in your head once the scale is fixed. One percent is 100 basis points, one tenth of a percent is 10 basis points, and one basis point is a hundredth of a percent. Everything else is a multiplication or a division by 100.

Basis points, percent and percentage points

Three quantities get mixed up, and only one of them is a basis point problem:

• A percentage point is the plain difference between two percentages. 6.75 minus 6.50 is 0.25 of a percentage point.
• A percent change compares that difference to the starting value. 0.25 divided by 6.50 is a 3.8462 percent increase.
• A basis point is the percentage point difference multiplied by 100. That same 0.25 point move is 25 bp.

The distinction matters most in the middle of the range. A fund fee going from 0.03 percent to 0.06 percent has doubled, which sounds alarming, yet the change is 3 basis points. A mortgage rate going from 6.50 percent to 6.75 percent is only a 3.8462 percent increase in the rate itself, but borrowers feel it as 25 bp because the payment is what they pay.

The parts per million column is the one people forget. It is useful for fees and for pollution limits, and it follows the same pattern: 1 bp is 100 ppm, because 1 percent is 10,000 ppm and 1 bp is one hundredth of 1 percent.

Why the Fed and bond desks count in basis points

Policy statements are written in basis points because the decisions themselves are that small. The Federal Reserve's July 2024 Monetary Policy Report describes the tightening cycle that began in early 2022 as a total increase of 525 basis points in the target range, which took it from near zero to 5-1/4 to 5-1/2 percent. The same report notes the committee then held that range steady for a year.

The 2024 Federal Reserve Annual Report records the other direction: a cumulative 100 basis points of cuts across the September, November and December 2024 meetings, which brought the range to 4-1/4 to 4-1/2 percent. A quarter point cut is 25 bp, and a half point cut is 50 bp, which is how those meetings were reported at the time.

Bond desks use the same unit for a different reason. A Treasury yield quoted to two decimals is too coarse when a fund holds millions of dollars of duration, since one basis point on a large position is real money. Quoting in bp also lets a trader compare a yield move to a spread without converting anything: a bond yielding 4.35 percent against a benchmark at 4.10 percent carries a 25 bp spread, no arithmetic required.

Worked example: 25 basis points on a $320,000 mortgage

A 25 bp move looks trivial until it meets a 30 year balance. Take a $320,000 loan at 6.50 percent, which is a monthly rate of 0.0054167 and 360 payments. The standard amortization formula gives a payment of $2,022.62. Raise the rate by 25 bp to 6.75 percent and the payment becomes $2,075.51.

The difference is $52.90 a month. Over the full 360 payments it adds up to $19,042.64, which is roughly the price of a used car for a quarter of a percentage point. The same move in the other direction, from 6.50 down to 6.25, saves $52.32 a month, slightly less than the rise costs, because the formula is not linear.

Interest totals dwarf the loan. At 6.50 percent the borrower pays $728,142.36 over 30 years, more than twice the amount borrowed, which is why a 25 bp difference is worth shopping for. The calculator above shows the same numbers when you enter the loan amount, the rate and the change in bp.

Worked example: 50 basis points on a bond price

Bond prices move the other way from yields. When the yield on a bond rises, the fixed interest payments it makes are worth less, so the price falls. The size of the fall depends on modified duration, which measures how many years of cash flow the bond still has, weighted by when the money arrives.

A bond priced at $1,000 with a modified duration of 6.5 years faces a yield rise of 50 bp. The duration approximation says the price change is minus duration times the yield change: 6.5 years x 0.005 gives -3.25 percent, or -$32.50, and the bond is worth $967.50. Move the yield the other way and 50 bp down gives +3.25 percent, so the price rises to $1,032.50.

Duration also scales the reaction. A 10 year duration would have lost 5 percent on the same 50 bp move, which is $50 per $1,000 of face value, and a 4 year duration would have lost only 2 percent. That is why long bonds are described as riskier even when the coupon is the same: more duration means more price per basis point.

The approximation is close for small moves and drifts as the move grows, because price and yield curve rather than run in a straight line. For a 100 bp move on a 6.5 duration bond, the true price is a little higher than $935.00, and the gap is the convexity the linear estimate ignores.

Fees, spreads and yields in basis points

Fund companies quote expense ratios in basis points because the numbers would look like rounding errors as percentages. An index fund charging 0.03 percent is charging 3 bp. On a $10,000 balance that is $3.00 a year, and on $250,000 it is $75.00. An actively managed fund at 0.75 percent is 75 bp, which is $1,875.00 a year on $250,000, and that difference compounds against the investor every year.

The same arithmetic turns any rate into dollars. Multiply the balance by the basis points and divide by 10,000. For a 25 bp spread on $250,000, that is 250,000 x 25 / 10,000, which comes to $625.00 a year, or $52.08 a month. This is the check worth running when a lender quotes a rate in bp and you want to know what it costs in money you can spend.

Credit cards and savings accounts use the same scale. A card at 24.99 percent that rises 50 bp is at 25.49 percent, and a savings account at 4.25 percent that falls 25 bp is at 4.00 percent. Neither move sounds like much, and on a $5,000 balance that is $25 a year, which is exactly why banks advertise in one direction and bury the other.

Converting in both directions without a mistake

Two conversions cover almost every case, and they run in opposite directions:

• Percent to basis points: multiply by 100. A rate of 4.35 percent is 435 bp.
• Basis points to percent: divide by 100. A move of 37 bp is 0.37 percent.

The common error is moving the decimal one place instead of two. A 4.35 percent rate is 435 bp, not 43.5 bp, and 43.5 bp is 0.435 percent, which is a different instrument entirely. The other common error is writing a move of 0.25 percent as 0.25 bp, which understates it by a factor of 100.

When the number is small, work in bp and convert at the end. A portfolio yielding 4.12 percent that gains 8 bp is at 4.20 percent, because 8 bp is 0.08 percent. Doing it the other way, converting to percent first and adding, invites a dropped zero in the middle of the arithmetic.

One more check helps with quoted spreads. If a bond yields 5.62 percent and the benchmark yields 5.30 percent, the spread is 0.32 percent, which is 32 bp. Subtract the yields first, then multiply by 100, and the answer lands in the right units every time.

Where the numbers stop being precise

The loan figures on this page come from the standard amortization formula, so they are exact for a fixed rate loan with equal payments and no fees. Real mortgages add property tax escrow, insurance, private mortgage insurance and origination points, and each of those shifts the payment without changing the rate. The bp change is still the right way to compare two quotes, as long as both quotes carry the same fees.

The bond figures are an approximation, and the page says so. Modified duration gives a straight line estimate of a curved relationship, so it overstates the loss when yields rise and understates the gain when they fall. For a 50 bp move the error is small. For a 200 bp move it is large enough that a trader would add a convexity term, and for a callable bond or a mortgage backed security the cash flows themselves change when rates move, which breaks the assumption that duration is constant.

Adjustable rate loans break it in a different way. A 25 bp move in the index may not pass through at all in a given year, because caps limit how much the rate can change per period and over the life of the loan. The bp arithmetic still applies to the index, and the cap decides how much of it reaches your payment.