Treasury Bill Calculator
The formula
What the t-bill return tells you
Buying a Treasury bill at discount and collecting face at maturity — the risk-free rate with a state-tax bonus attached.
Calculation: Price = face × (1 − discount × days/360); bond-equivalent yield annualizes it. Enter your inputs and every substitution is shown below the result.
Reading the result
Compare bills to CDs and money funds on after-tax yield: the state exemption is worth 1–5% of the rate depending where you live.
Rules of thumb: Bills track fed funds ±25bps across the curve; $100 minimum denominations
Limitations and best practice
The quoted discount rate understates the yield you actually earn — BEY is the comparison number, and prices move between auction and sale.
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
Are T-bills really risk-free?
What about the new 4-week bills?
Source & methodology
TreasuryDirect auction conventions; BEY formula standard.
Treasury Bill explained: formula, worked example and honest limits
This page was written for one job: turning your own inputs into a defensible figure, with the working shown. There are plenty of pages about Treasury Bill; almost none of them show the working. This one does: the formula, every input, a fully computed example, and a sensitivity analysis calculated live from this engine’s own defaults.
In plain terms, Treasury Bill answers the question "T-bill purchase price?". 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 Finance & Banking, Savings & Budgeting is the context where this figure is quoted most often, and professionals treat it as a first-pass screen rather than a verdict.
There is a habit that separates people who get useful answers from Savings & Budgeting numbers: they decide what question the figure answers before they compute it. Treasury Bill answers “T-bill purchase price?” — and nothing else, which is precisely why the result is trustworthy.
What makes a calculation page trustworthy is that its copy is derived from its own arithmetic: here t-bill purchase price = $19,094, recomputed every time a field changes, and the sensitivity section ranks the inputs that move the result — Face value first, at ≈10.0 % of the headline for a ten-percent error either way in that input. Work down the page and by the end you could re-derive the result in a spreadsheet from memory.
Inside the Treasury Bill calculation: formula and every input
Here is the complete model this tool runs — Price = face × (1 − discount × days/360); bond-equivalent yield annualizes it — with each input explained below. If a competitor’s page gives you a different answer from the same inputs, this is the text that settles which of you is right.
Face value ($) (example value 19,500) is a measured number in the unit named by the label; the formula does not convert for you. This input feeds the formula directly; a defensible figure here is worth more than false precision anywhere else.
Discount rate (%) (example value 5) is a measured number in the unit named by the label; the formula does not convert for you. Check the convention first: if the source says “6.5 % per year”, type 6.5 and let the formula do the rest.
Term (weeks) (example value 21) is a quantity rather than a category — precision here is cheap and worth having. Use the value as of today, not as of the last time you looked — time fields drift silently.
A fully worked Treasury Bill example
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: Face value ($), Discount rate (%), Term (weeks). The computed t-bill purchase price comes out at $19,094, which the interpretation band labels “Pay $19,094 now, collect $19,500 in 21 weeks — 5.28% bond-equivalent yield, exempt from state tax”.
- Price = $19,500 × (1 − 5.1% × 147/360) = $19,094
- BEY = ($19,500 − $19,094) ÷ $19,094 × 365/147 = 5.28%
Gain at maturity — $406. Compare it against the main result of $19,094 before drawing conclusions.
Bond-equivalent yield — 5.28 %. If your inputs change, this is usually the first companion figure to move.
Investment for $100k face — $190,939. Compare it against the main result of $19,094 before drawing conclusions.
After-tax equivalent at 5% state rate — 5.56 %. This is the number experienced users quote when the headline alone would mislead.
Overwrite any input above and every line of this example updates with it — the substitution is live, not a screenshot of somebody else’s numbers.
The Treasury Bill corridor: your result across a realistic band
Read this table as the practical error bar on the headline figure. It answers the question people actually have after seeing a single number: how wrong could this be if the main input is off by ten or twenty percent?
| Face value setting | T-bill purchase price |
|---|---|
| 80 % of the example value | $15,275 |
| 90 % of the example value | $17,185 |
| example inputs | $19,094 |
| 110 % of the example value | $21,003 |
| 120 % of the example value | $22,913 |
That spread — $15,275 at the low end, $22,913 at the high — is what a careful read of Treasury Bill looks like: a band you can state out loud, with the reason for each edge. Reproduce it in the form above by editing Face value alone; the substitution steps will follow your figures exactly.
Sensitivity: which inputs change Treasury Bill the most
This list was computed for this specific engine just now: each numeric input was nudged ±10 % while every other field held its example value, and the t-bill purchase price was recalculated from scratch. For Treasury Bill the ranking is measured rather than guessed, and it belongs to these defaults: shift the starting point and the order can shift with it.
- Face value +10 % → Treasury Bill = $21,003 · −10 % → $17,185 (the t-bill purchase price shifts ≈10.0 %)
- Discount rate: ten percent up gives $19,053, ten percent down gives $19,135 — ≈0.2 % of the t-bill purchase price either way
- Nudge Term by ±10 % and Treasury Bill lands between $19,053 and $19,135 (sensitivity ≈0.2 %)
Face value is the dominant lever here: ten percent either way moves the result by about 10.0 %, from $17,185 to $21,003. Measure that input from a document rather than from memory, and treat Discount rate as the second priority (≈0.2 % per ten percent). The rest of the inputs earn only a rounding-error of attention, and that asymmetry is the practical payoff of measuring rather than asserting.
Interpreting the Treasury Bill verdict
A number on its own is trivia; a number against a range is intelligence. The default case lands in the “Pay $19,094 now, collect $19,500 in 21 weeks — 5.28% bond-equivalent yield, exempt from state tax” band, and bands are deliberately wide because real situations overlap. The sensitivity list shows how far a modest input error moves you along that ladder: for Face value, ±10 % covers $17,185 to $21,003. The practical reading rules: ask what would have to change to move you one band. If the answer is “a small, plausible input difference”, the band itself is not the finding — the uncertainty is.
Where Treasury Bill sits next to similar measures: this tool answers “how much is the Treasury Bill”, while the related calculators answer “what do I do about it”. Reading the result alone tends to over-weight a single snapshot; pairing it with the companion tools above turns the number into a decision.
The errors that quietly break a Treasury Bill figure
The quoted discount rate understates the yield you actually earn — BEY is the comparison number, and prices move between auction and sale. 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 Treasury Bill begins the moment your own figures replace them.
One mistake is specific to this engine: assuming every input matters equally. The computation above shows Face value dominating — a careful figure there beats false precision everywhere else.
A final trap is presentation: reporting Treasury Bill to more decimal places than the inputs support. The tool prints what the arithmetic gives; you should quote only what your least precise field justifies.
Before you trust your Treasury Bill: a short checklist
- Check whether the formula treats your inputs as nominal or real dollars.
- Verify each input against its original source document, not memory.
- Re-verify Face value against a source document — ten percent of error there moves the headline by ≈10.0 %.
- Confirm the example values are plausible for your own situation before replacing them.
- Confirm rate conventions (APR vs effective, day-count) before comparing two offers.
- Run the ±10 % stress on the top two levers and check that your conclusion survives both.
How to use the Treasury Bill 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 — collect, then type. Everything this tool asks for is listed above (face value ($), discount rate (%), term (weeks)). Pull each figure from something you can point at — paperwork, a dashboard, a label — before touching a field. Guesswork at the input stage cannot be repaired at the interpretation stage. The fastest sanity test is to guess the answer first and see how far the calculation disagrees.
Step 2 — baseline before exploration. Get one defensible T-bill purchase price on screen before you start nudging numbers. Without a baseline, every variation looks interesting and none of them means anything. Suspiciously tidy answers deserve the same scrutiny as untidy ones.
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. Suspiciously tidy answers deserve the same scrutiny as untidy ones.
Step 4 — stress before you commit. A decision that survives a ten-percent squeeze on its two biggest inputs needs no luck to be sound. One that does not survive is a decision about hope, not about arithmetic. When two sources disagree, it is almost never the arithmetic that differs.
Step 5 — write the one-line memo. “T-bill purchase price = $19,094 on this date, from these inputs.” That line is the entire deliverable; everything else on this page is how you earned the right to write it. Estimates improve most when the worst case is written down in ink.
Where Treasury Bill matters in practice
In Savings & Budgeting the figure computed here is usually the first one somebody asks to see. Having it — with the formula behind it — changes your position in the conversation from participant to reference. A figure nobody can reproduce is a figure nobody will act on twice.
Professionals in Savings & Budgeting use this style of calculation as a screening filter before spending real money or effort: a quick Treasury Bill check eliminates weak options in minutes, and the survivors earn the deeper, slower analysis. Note the assumption you are least sure about; that is where the real risk lives.
Re-running this page costs nothing and catches the slow drifts that never announce themselves. In Finance & Banking the expensive mistakes are rarely sudden; they are small changes in Face value ($) that nobody recalculated for a year. A calculation you cannot explain to somebody else is a calculation you cannot defend.
The questions that come up most about Treasury Bill
What affects Treasury Bill the most?
Treasury Bill is driven above all by Face value. Perturbing only that field by ten percent either way produced $21,003 against the $19,094 baseline — a ≈10.0 % response, while Discount rate manages ≈0.2 %.
Which matters more: discount rate or face value?
By the numbers, Face value: a ten-percent change in it moves the result ≈10.0 %, versus ≈0.2 % for Discount rate. Spend your measuring effort in that order — precision on the weaker lever buys almost nothing.
What is a typical Treasury Bill?
There is no honest universal average for Treasury Bill, but there is a reference point: the defaults on this page produce $19,094 (Pay $19,094 now, collect $19,500 in 21 weeks — 5.28% bond-equivalent yield, exempt from state tax). Replace the inputs with your own and compare — that comparison is the useful meaning of “typical”.
How do I calculate Treasury Bill by hand?
Three steps: write the formula (Price = face × (1 − discount × days/360); bond-equivalent yield annualizes it), insert your values, and simplify. The worked example section shows exactly that chain for the default inputs; replicating it once on paper teaches you more about Treasury Bill than any number of calculator runs.
What happens to Treasury Bill if face value changes by 10 %?
Try it in the form above and the printed substitution will follow you; the pre-computed answer for the defaults is $17,185 to $21,003 across the ten-percent probe, i.e. ≈10.0 % sensitivity on the t-bill purchase price.
Is the Treasury Bill result of $19,094 good or bad?
Neither, on its own — the label “Pay $19,094 now, collect $19,500 in 21 weeks — 5.28% bond-equivalent yield, exempt from state tax” 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 Face value alone moves it by ≈10.0 %.
Is Treasury Bill accurate?
The arithmetic is exact: Price = face × (1 − discount × days/360); bond-equivalent yield annualizes it 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 $19,094 result as the correct answer to the question you typed — and check the assumptions section before acting on it.
Should I use Treasury Bill for large purchases?
Yes — big purchases should never clear on gut feel. Run the number here, then stress the two biggest inputs; a decision that survives a ±10 % squeeze is genuinely solid.
Are T-bills really risk-free?
Default-risk-free in nominal terms; holding to maturity removes price risk — selling early reintroduces it.
What about the new 4-week bills?
Shorter terms track the policy rate tightly and roll more often — the discount arithmetic is unchanged.
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.
Glossary for Treasury Bill
- Gain at maturity
- $406 in the default Treasury Bill calculation — one of the secondary figures an experienced reader checks before trusting the primary number.
- Bond-equivalent yield
- 5.28 % for the Treasury Bill worked case; it sits next to the main result because it carries context the headline leaves out.
- Investment for $100k face
- $190,939 in the default Treasury Bill calculation — one of the secondary figures an experienced reader checks before trusting the primary number.
- T-bill purchase price
- The primary output of this tool: $19,094 for the default inputs, computed exactly from Price = face × (1 − discount × days/360); bond-equivalent yield annualizes it.
- Worked example
- The calculation written out in full so that nothing on this page has to be taken on trust.
- Verdict band
- The interpretation attached to a result (“Pay $19,094 now, collect $19,500 in 21 weeks — 5.28% bond-equivalent yield, exempt from state tax” on these inputs), which turns a bare number into a position on a scale.
- Sensitivity (±10 %)
- How far the Treasury Bill moves when a single input is nudged ten percent either way; the ranked list on this page is computed live from this engine.
Method, sources and what this tool cannot tell you
The model is published arithmetic implemented exactly as written: Price = face × (1 − discount × days/360); bond-equivalent yield annualizes it. Source of record: TreasuryDirect auction conventions; BEY formula standard. Any other implementation of this model should return the same figure for the same inputs. If one does not, the difference is in its assumptions — which this page prints and that one probably does not.
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. The design constraint was set by usefulness rather than by comfort: an estimate you can interrogate beats an answer you have to trust.
Turning this Treasury Bill into a decision
Re-run the calculation with your own figures, stress the two most sensitive inputs by ±10 %, and only then act on the result.
The audience here is people who need one trustworthy number before their next decision. Everything you need to defend the result — formula, substitution, sensitivity, source — is printed above, so the only remaining variable is the honesty of your inputs.