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CalcMax

Basis Point Calculator

Range: -1,000,000 – 1,000,000

Result

800.00

Basis points (bp)

As a percentage (%)
8.0000%
As a decimal
0.080000

A basis point calculator converts one rate into three notations. Enter a number, say which of the three units it is in — percent, basis points, or a plain decimal — and the page returns the same quantity written the other two ways, plus that rate in parts per million. One basis point is one hundredth of a percentage point, which is 0.01 percent, which is 0.0001 as a decimal, which is 100 parts per million. So eight percent is 800 basis points, and a quarter of a percentage point is 25 of them. Nothing about the rate changes when you change the unit; the unit is a way of writing the number and not a fact about it. The reason basis points exist is that the alternatives are ambiguous. A quarter of a percent, said aloud, could be 0.25 of a percentage point or a quarter of the rate itself — two numbers that differ by a factor of four hundred at an 8 percent rate. Twenty-five basis points means one thing, and it means the same thing to everyone in the room. That precision only matters when rates are small and the sums they apply to are not. Half a percentage point on a credit card balance is worth arguing about and 50 basis points is how the argument gets settled; on a 500,000 balance a 25 basis point move is 1,250 a year, which is why a market that moves in 25 basis point steps is moving real money even when the move sounds like nothing. Three things about the page are worth knowing. It accepts negative numbers, because a spread or a yield differential can be negative and so can a rate in jurisdictions that allow one, and the conversion is symmetric in sign. Its working range is a thousand percent down and up — 100,000 basis points, or 10 as a decimal — and the input box itself accepts up to a million of whatever unit you picked, so a number outside the meaningful range produces an error message rather than a figure. And the parts per million figure is a fourth notation for the same ratio, useful when the rate is being applied to a notional amount rather than quoted: one basis point is 100 per million, so a 25 basis point fee on a notional is 2,500 per million of it. What this page does not do is tell you what any of it is worth. It converts a rate; it does not apply one. Twenty-five basis points against a balance, over a term, with or without compounding, is a different question with different pages — the interest rate calculator solves a rate out of a payment, the annual percentage rate calculator adds fees to one. This page is the step before those: making sure the number you are about to type into them is the number you meant.

The same rate written three ways, from one basis point to a full point

PercentBasis pointsPer million
0.011100
0.055500
0.1101000
0.25252500
0.5505000
110010000

Every row is one ratio in three notations, so the table is not a series of results but a set of translations. The bottom row is the smallest step that has a name — a single basis point, a hundredth of a percentage point — and the top row is a whole point, a hundred of them. The range was chosen because it covers where mortgage rates, policy rates and bond spreads actually live: a rate quoted to two decimal places of a percent is quoted to single basis points, which is the precision the unit was invented to make speakable. The third column is the same number again expressed per million, which is the form that becomes useful the moment the rate is applied to a notional: read the bottom row as one basis point being 100 per million of whatever the rate is charged on, so a 25 basis point spread is 2,500 per million. Nothing in this table depends on a principal, a term or a currency, and that is the point of the page it belongs to.

Formula

Basis points = percent × 100 Percent = basis points ÷ 100 Decimal = percent ÷ 100 Per million = decimal × 1,000,000

Rate value
The number itself, in whichever of the three units you selected — 8, 800 or 0.08 all describe the same rate, and the page's job is to say so
Unit
Which of the three notations the number is written in: percent, basis points, or a decimal fraction. It is a statement about the notation and not about the rate, which is why changing it alone changes nothing about the answer
Basis points
The rate in hundredths of a percentage point — the unit central banks and bond desks quote moves in, and the one that removes the ambiguity of saying a quarter of a percent out loud
Percent
The rate as people say it, in percentage points: 0.25 means a quarter of a percentage point, not a quarter of the rate
Decimal
The rate as arithmetic needs it — the fraction to multiply a balance by, so 0.0025 rather than 0.25. This is the form that goes into every other calculator in this group

Use it whenever a rate arrives in a unit you do not think in. Three cases cover almost everything. Reading a policy decision or a market story that moves in basis points: 25 basis points is 0.25 of a percentage point, so a 5 percent rate that rises 25 basis points becomes 5.25 percent — and the common mistake is reading 25 basis points as 0.25 percent of 5 percent, which would be 5.0125 percent. Comparing a quoted spread against a rate you already know: a bond yielding 4.35 percent and a benchmark at 4.10 percent differ by 25 basis points, which is a spread of a quarter of a point and not a quarter of the yield. And preparing a number for another calculator, where the decimal form is what the arithmetic wants: a 0.0025 decimal is the figure that multiplies a balance to produce a quarter point of interest, and entering 0.25 there instead would overstate the result a hundredfold. A fourth case is the one that catches people out on large numbers. When a rate change is quoted in basis points and you want to know what it costs, the conversion is only the first step: 25 basis points is 0.0025 as a decimal, and only then does multiplying by the balance produce money. Doing those two steps in the wrong order — treating 25 basis points as 0.25 — is the error this page exists to prevent, and on a 500,000 balance it is the difference between 1,250 and 125,000.

Worked examples

  1. 8 percent, written three ways

    1. Basis points: 8 × 100 = 800
    2. Percent: 8, unchanged — it went in as a percent
    3. Decimal: 8 ÷ 100 = 0.08
    4. Per million: 0.08 × 1,000,000 = 80,000

    The default case, and the one the regulator's own glossary uses as its example. The three outputs are one number: 8 percent is 800 basis points is 0.08. Read the third one carefully, because it is the form the rest of this group expects — every other page here multiplies a balance by the decimal, so 0.08 is the number to carry forward and 8 is the number to say out loud.

  2. 25 basis points — the unit policy moves in

    1. Percent: 25 ÷ 100 = 0.25
    2. Decimal: 0.25 ÷ 100 = 0.0025
    3. Basis points: 25, unchanged — it went in as basis points
    4. Per million: 0.0025 × 1,000,000 = 2,500

    The classic quarter-point move, and the case where the two readings of a quarter of a percent diverge. If a 5 percent rate rises by 25 basis points it becomes 5.25 percent; if it rose by a quarter of itself it would become 5.0125 percent. The decimal form is what settles it: 0.0025 is the fraction of a balance that 25 basis points represents, so 500,000 earns 1,250 more a year — not 125,000.

  3. The same 8 percent entered as a decimal

    1. Percent: 0.08 × 100 = 8
    2. Basis points: 8 × 100 = 800
    3. Decimal: 0.08, unchanged — it went in as a decimal
    4. Per million: 0.08 × 1,000,000 = 80,000

    Identical to the first example, from a different starting unit — which is the point of the page. The unit is a label on the number, not part of it; entering 0.08 as a decimal and 8 as a percent are two ways of asking the same question, and the panel answers both the same way. If the outputs ever differed, the page would be broken rather than clever.

Limitations

It converts units and nothing else. It does not apply the rate to any amount, so it cannot tell you what a basis point move costs on a balance, over a term, or after compounding — those are the sibling pages, and this one deliberately has no principal field. It does not know whether the number you entered is an annual rate, a monthly rate or a spread; the conversion is the same in every case, and it is up to you to know which one you have, because feeding a monthly rate into an annual calculation is a mistake no unit converter can catch. It does not model the quoting conventions of particular markets: in foreign exchange a basis point is usually 0.0001 but is 0.01 for yen-quoted pairs, and some markets quote in fractions of a point rather than in basis points at all, so a number taken from a trading screen may not mean what this page assumes. The working range is a thousand percent in either direction — 100,000 basis points, or 10 as a decimal — and the input field itself will accept up to a million in whichever unit you chose, which means a plausible-looking entry like 1,500 percent passes the field and then fails in the calculation. The error message is deliberate: a rate above a thousand percent is not impossible, but it is not something this converter is willing to launder into a tidy answer without saying so. And it reports the ratio to a fixed number of decimals — four for the percent form, six for the decimal — so a rate smaller than 0.00005 of a percentage point will print as zero rather than as the fraction it is.

Frequently asked questions

What is a basis point?
One hundredth of a percentage point: 0.01 percent, or 0.0001 as a decimal, or 100 parts per million. Eight percent is 800 basis points and a quarter of a percentage point is 25. The unit exists because a quarter of a percent spoken aloud is ambiguous — it could mean a quarter of a percentage point or a quarter of the rate — and basis points remove the ambiguity.
How do I convert basis points to a percentage?
Divide by a hundred. Twenty-five basis points is 0.25 of a percentage point, 50 is half a point, and 100 is a full point. Going the other way, multiply the percentage by a hundred: 5.25 percent is 525 basis points. To get the decimal form used in arithmetic, divide by a hundred again, so 25 basis points is 0.0025.
Why do people say basis points instead of percentages?
Because on small rates the percentages get ambiguous, and because the numbers stay readable. A rate rising from 0.5 percent to 0.75 percent has risen by 50 percent of itself and by 25 basis points; both statements are true and only one of them is useful in a conversation about policy. Basis points also keep the arithmetic clean on large notional amounts, where a move of 25 basis points is 2,500 per million — a figure that stays legible where 0.0025 does not.
Can a basis point value be negative?
Yes. A spread between two yields can be negative when the bond yields less than its benchmark, and a policy rate can be negative in the jurisdictions that have gone below zero. This page converts negative numbers symmetrically — minus 25 basis points is minus 0.25 percent and minus 0.0025 as a decimal — because the conversion is a change of notation and signs survive it unchanged.
How much money is a basis point worth?
This page cannot tell you, and that is deliberate: it has no balance field. One basis point is 0.0001 as a decimal, so on a balance of 1,000,000 it is 100 a year before compounding, and on 500,000 it is 50. Multiply the balance by the decimal form and you have your answer — but that multiplication belongs to the pages that model money and time, and this one stops short of it so that the conversion cannot be confused with a calculation.
Is a basis point the same as a pip?
Not quite, though they are used in the same way. A basis point is defined as 0.0001 of the quantity being measured, which is a fixed fraction. In foreign exchange a pip is also usually 0.0001, but for pairs quoted in yen it is 0.01, so the two terms coincide most of the time and not always. When a rate is quoted in basis points the meaning is unambiguous; when a currency is quoted in pips it depends on the pair.

References

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