Dirty Price Calculator
The formula
What the dirty price tells you
The real money that changes hands. Quotations are clean for comparability across coupons, but settlement is dirty — accrued interest goes to the seller.
Calculation: Dirty price = clean + accrued; invoice = dirty ÷ 100 × face. Enter your inputs and every substitution is shown below the result.
Reading the result
Yield engines must run on dirty prices; quoting on clean is a convention that would corrupt any IRR if applied literally.
Rules of thumb: Plumbing, not judgment — but check basis conventions
Limitations and best practice
Tax detail worth knowing: you pay accrued as part of principal but recover it tax-free via the next coupon — misbooked, it distorts cost basis.
This calculator gives an estimate based on standard formulas; it is not professional financial, medical, legal or engineering advice. Verify anything you plan to act on with a qualified professional and your own records.
Frequently asked questions
Who sets the accrued convention?
Why do yield calculations use the dirty price?
Source & methodology
SIFMA clean/dirty price convention.
Dirty Price: the number, the method and the caveats
You are sizing a cost, and the difference between a rough guess and a computed estimate is exactly what this page provides. Dirty Price is the kind of number people argue about from memory. This page ends that argument with arithmetic you can watch happen: enter your figures, get Dirty (invoice) price per $100 in real time, and see every substitution printed below.
Most confusion about Dirty Price comes from mixing up the input you control with the input you merely observe. The formula treats them identically, but your decisions should not: one deserves measurement, the other deserves a defensible estimate.
In plain terms, Dirty Price answers the question "Dirty (invoice) price per $100?". The measurement matters because it converts a situation that feels complicated — several inputs pulling in different directions — into a single number you can act on. Within Investing & Markets, Fixed Income is the context where this figure is quoted most often, and professionals treat it as a first-pass screen rather than a verdict.
Every figure in the prose is generated by the engine rather than written beside it — the worked example resolves to dirty (invoice) price per $100 = 72.850 on the default inputs, and the sensitivity section ranks the inputs that move the result — Clean quoted price per $100 first, at ≈9.7 % of the headline for a ten-percent error either way in that input. Read the sections in order and you will be able to reproduce every figure by hand.
How Dirty Price is computed, line by line
Here is the complete model this tool runs — Dirty price = clean + accrued; invoice = dirty ÷ 100 × face — with each input explained below. If a competitor’s page gives you a different answer from the same inputs, this is the text that settles which of you is right.
Clean quoted price per $100 (example value 71) is a plain measured quantity — the unit shown in the label is the unit the formula expects. Use the figure exactly as the source document states it, not a rounded memory of it — an omitted line is the classic silent error.
Accrued interest per $100 (example value 2) is a plain measured quantity — the unit shown in the label is the unit the formula expects. Rates are the most mis-transcribed input on any page like this; copy it from the document rather than retyping from memory.
Face amount you are buying ($) (example value 117,500) is a quantity rather than a category — precision here is cheap and worth having. Keep every money input in the same currency; mixing systems quietly corrupts the comparison.
The default Dirty Price calculation, written out in full
Abstract formulas are hard to trust, so here is the complete substitution using the default inputs, written the way an examiner would want it. Starting figures: Clean quoted price per $100, Accrued interest per $100, Face amount you are buying ($). Run to the end, the dirty (invoice) price per $100 resolves to 72.850 — Cash outlay on $117,500 face: $85,599 on the bands this tool uses.
- Dirty = 71 + 1.85 = 72.850 per 100
- Invoice = 72.850 ÷ 100 × $117,500 = $85,599
Cash required — $85,598.75. If your inputs change, this is usually the first companion figure to move.
Accrued portion of invoice — 2.54 %. This is the number experienced users quote when the headline alone would mislead.
Per $1,000 bond — 728.50 $. Compare it against the main result of 72.850 before drawing conclusions.
Keep this worked example open while you enter your own figures: matching the shape of the substitution is the fastest way to spot a unit or convention mistake.
Scenario table: Dirty Price at ±10 % and ±20 % of the key input
Single-point answers invite false confidence, so the same engine was run across a band around the input that matters most here. Each row is a full recalculation of Dirty Price, not an interpolation.
| Clean quoted price per $100 setting | Dirty (invoice) price per $100 |
|---|---|
| 80 % of the example value | 58.650 |
| 90 % of the example value | 65.750 |
| example inputs | 72.850 |
| 110 % of the example value | 79.950 |
| 120 % of the example value | 87.050 |
That spread — 58.650 at the low end, 87.050 at the high — is what a careful read of Dirty Price looks like: a band you can state out loud, with the reason for each edge. Reproduce it in the form above by editing Clean quoted price per $100 alone; the substitution steps will follow your figures exactly.
Where Dirty Price is fragile — and where it is not
Nobody should have to guess which input matters. The engine was re-run once per field below — ten percent up, ten percent down, everything else frozen — and the results ranked by how far they moved the dirty (invoice) price per $100. For Dirty Price the ranking is measured rather than guessed, and it belongs to these defaults: shift the starting point and the order can shift with it.
- Nudge Clean quoted price per $100 by ±10 % and Dirty Price lands between 65.750 and 79.950 (sensitivity ≈9.7 %)
- Accrued interest per $100 +10 % → Dirty Price = 73.035 · −10 % → 72.665 (the dirty (invoice) price per $100 shifts ≈0.3 %)
Clean quoted price per $100 is the dominant lever here: ten percent either way moves the result by about 9.7 %, from 65.750 to 79.950. That is where a careless figure does the most damage, so check it against a source, and treat Accrued interest per $100 as the second priority (≈0.3 % per ten percent). Everything below that can stay approximate, which is a licence to stop chasing data that would not change the decision.
Interpreting the Dirty Price verdict
A number on its own is trivia; a number against a range is intelligence. The default case lands in the “Cash outlay on $117,500 face: $85,599” band, and bands are deliberately wide because real situations overlap. Before treating the band as fact, note its width: ten percent either way on Clean quoted price per $100 already spans 65.750 to 79.950. The practical reading rules: read the band as a starting hypothesis, then test it: change the two dominant inputs by ten percent and see whether the verdict survives. Verdicts that survive stress are the ones worth acting on.
Compared with charting sites, this page explains the formula rather than hiding it — the goal is a number you can defend in a meeting, not just display.
How people get Dirty Price wrong
Tax detail worth knowing: you pay accrued as part of principal but recover it tax-free via the next coupon — misbooked, it distorts cost basis. This calculator gives an estimate based on standard formulas; it is not professional financial, medical, legal or engineering advice. Verify anything you plan to act on with a qualified professional and your own records.
Treating the example inputs as a recommendation. They are a demonstration of the mechanism — a decision-grade Dirty Price begins the moment your own figures replace them.
This model has its own particular trap: Clean quoted price per $100 carries ≈9.7 % of the response per ten percent of error, so effort spent elsewhere is largely decorative.
Another is comparing across contexts: a Dirty Price computed with one set of conventions should never be lined up against a figure computed with another. Check the inputs behind both before ranking them.
Dirty Price verification checklist
- Compare the result with one independent method or published benchmark.
- Compare the output against one published benchmark or a colleague’s independent estimate.
- Put Clean quoted price per $100 under a magnifier; the sensitivity table above is the reason why.
- Check that every field the formula needs actually arrived from a document, not from recollection.
- Recompute once with the dominant input deliberately set low, and see whether the decision changes.
- Run the ±10 % stress on the top two levers and check that your conclusion survives both.
How to use the Dirty Price tool properly
The tool does the arithmetic; the routine below is what makes the arithmetic trustworthy. Five steps, a minute total — and afterwards you will know not just what the number is, but which assumption produced it.
Step 1 — start from evidence. The inputs behind Dirty Price are clean quoted price per $100, accrued interest per $100, face amount you are buying ($). Write them down with their source next to each one; if you cannot name where a figure came from, that is the input most likely to be wrong. A figure nobody can reproduce is a figure nobody will act on twice.
Step 2 — baseline before exploration. Get one defensible Dirty (invoice) price per $100 on screen before you start nudging numbers. Without a baseline, every variation looks interesting and none of them means anything. When two sources disagree, it is almost never the arithmetic that differs.
Step 3 — measure what deserves measuring. The ranked levers above tell you where a careful figure pays off. Everything else can stay approximate, which is a licence to stop hunting for data you do not need. The test of a good estimate is not that it feels right but that it changes what you do.
Step 4 — ask what would have to be true. Take the result you want and work backwards through the inputs until you find the assumption that produces it; then decide honestly whether that assumption is defensible. Precision is a promise you make about your data; make sure your inputs can keep it.
Step 5 — save the story with the figure. A number without its inputs and its date is unusable within a quarter. Record 72.850, the assumptions behind it, and today’s date; your future self will be auditing a stranger’s arithmetic. The inputs are the part of the work that nobody else can do for you.
Where Dirty Price matters in practice
Investing & Markets arguments end at arithmetic or they do not end. Dirty Price is the arithmetic: 72.850 on the example inputs, reproducible by anyone who types the same numbers. Estimates improve most when the worst case is written down in ink.
Used properly this is a five-minute filter that saves weeks. Compute Dirty Price, reject what fails, and only then bring in the expensive analysis for the survivors. Say the answer out loud before you save it; if it sounds wrong, the model did not change, your understanding did.
Re-running this page costs nothing and catches the slow drifts that never announce themselves. In Investing & Markets the expensive mistakes are rarely sudden; they are small changes in Clean quoted price per $100 that nobody recalculated for a year. The test of a good estimate is not that it feels right but that it changes what you do.
The questions that come up most about Dirty Price
What affects Dirty Price the most?
The short answer: Clean quoted price per $100. The longer answer is the sensitivity table on this page, where every numeric input was probed by ten percent and the dirty (invoice) price per $100 recalculated — Clean quoted price per $100 moved it furthest, by roughly 9.7 % (65.750 to 79.950).
Which matters more: accrued interest per $100 or clean quoted price per $100?
By the numbers, Clean quoted price per $100: a ten-percent change in it moves the result ≈9.7 %, versus ≈0.3 % for Accrued interest per $100. Spend your measuring effort in that order — precision on the weaker lever buys almost nothing.
What is a typical Dirty Price?
On the worked example above Dirty Price comes out at 72.850. Treat that as one point on a distribution rather than a norm: the bands, the companion outputs and the sensitivity ranking tell you how wide the plausible range really is.
How do I calculate Dirty Price by hand?
Use the stated model — Dirty price = clean + accrued; invoice = dirty ÷ 100 × face — and substitute in the order the tool prints (it starts from Dirty = 71 + 1.85 = 72.850 per 100). On the example inputs the hand route lands on 72.850, exactly what the calculator shows. A spreadsheet reproduces it in two or three cells; doing it once by hand is what makes the automated answer trustworthy.
What happens to Dirty Price if clean quoted price per $100 changes by 10 %?
Try it in the form above and the printed substitution will follow you; the pre-computed answer for the defaults is 65.750 to 79.950 across the ten-percent probe, i.e. ≈9.7 % sensitivity on the dirty (invoice) price per $100.
Is the Dirty Price result of 72.850 good or bad?
Neither, on its own — the label “Cash outlay on $117,500 face: $85,599” is the band this figure falls in for the example inputs, and your own inputs will place you elsewhere on the same ladder. Judge the number against your history and your alternatives, and remember that a ten-percent error in Clean quoted price per $100 alone moves it by ≈9.7 %.
Is Dirty Price accurate?
The arithmetic is exact: Dirty price = clean + accrued; invoice = dirty ÷ 100 × face is evaluated with full floating-point precision and every substitution is printed in the worked example. What limits accuracy is input quality and the model’s assumptions, so treat the 72.850 result as the correct answer to the question you typed — and check the assumptions section before acting on it.
Can Dirty Price be negative or empty?
Yes, and that is informative rather than broken: a negative Dirty Price usually means the inputs encode an outflow or a shortfall, and the verdict band above labels exactly that situation instead of hiding it.
Who sets the accrued convention?
The exchange or the indenture: corporate 30/360, Treasury actual/actual. Your platform applies it automatically; verify with one sample trade.
Why do yield calculations use the dirty price?
Because the IRR must run on the cash you actually pay. Feeding a clean price into a yield formula understates your cost and overstates the yield.
Is my data private on this page?
Yes — computation happens locally in your browser, with no account, no tracking of your inputs and nothing sent to a server. The printed formula is the whole story of what happens to your figures.
Key terms on this page
- Cash required
- $85,598.75 for the Dirty Price worked case; it sits next to the main result because it carries context the headline leaves out.
- Accrued portion of invoice
- 2.54 % in the default Dirty Price calculation — one of the secondary figures an experienced reader checks before trusting the primary number.
- Per $1,000 bond
- 728.50 $ for the Dirty Price worked case; it sits next to the main result because it carries context the headline leaves out.
- Dirty (invoice) price per $100
- The primary output of this tool: 72.850 for the default inputs, computed exactly from Dirty price = clean + accrued; invoice = dirty ÷ 100 × face.
- Worked example
- The step-by-step substitution printed above, so the arithmetic can be re-derived by hand or in a spreadsheet.
- Verdict band
- The interpretation attached to a result (“Cash outlay on $117,500 face: $85,599” on these inputs), which turns a bare number into a position on a scale.
- Sensitivity (±10 %)
- How far the Dirty Price moves when a single input is nudged ten percent either way; the ranked list on this page is computed live from this engine.
Where the Dirty Price model comes from
The model is published arithmetic implemented exactly as written: Dirty price = clean + accrued; invoice = dirty ÷ 100 × face. Source of record: SIFMA clean/dirty price convention. Where a professional version of this calculation differs, it differs in inputs and jurisdiction-specific coefficients, not in the algebra — which is why re-checking your inputs beats hunting for a second calculator.
Nothing here replaces a qualified professional, and nothing here is approximate either — the arithmetic is exact, and the honesty is in the inputs you supply. Nothing is smoothed, weighted or adjusted behind the scenes; where judgement enters, this page says so and names the input responsible.
What to do with your Dirty Price next
Add the costs the estimate omits first — fees, waste, contingency — then re-run before treating the figure as a budget line.
Whoever you are (planners sizing a spend before committing money), the next step is the same: replace the example inputs with your own, note the date, and re-run whenever a figure moves. In Investing & Markets, a dated figure is a trend, and an undated one is a rumour.