Bond Equivalent Yield Calculator
The formula
What the bond equivalent yield tells you
T-bills and commercial paper are quoted as discount rates on face over a 360-day year — flattering nobody. BEY restates the instrument as a coupon-bond-style yield on a 365-day basis so you can compare it to bonds on the same screen.
Calculation: BEY = (365 × d) ÷ (360 − d × t). Enter your inputs and every substitution is shown below the result.
Reading the result
If the money-market rate and the short Treasury BEY diverge, one of them is carrying credit or liquidity premium — the gap is the signal.
Rules of thumb: Bills ≤ 1 year only; repos and CP quote separate conventions
Limitations and best practice
BEY annualizes simply, not geometrically — for maturities over one year the compounded (real) yield is slightly higher.
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
Why does the bill "yield" on my brokerage differ from the auction discount?
Why do 360 and 365 both appear in the formula?
Source & methodology
U.S. Treasury auction conventions; SEC money-market fund BEY rules (Rule 2a-7).
Bond Equivalent Yield explained: formula, worked example and honest limits
Capital decisions deserve better than a gut feeling — this page gives you the arithmetic to defend one. Searchers land on a Bond Equivalent Yield page for three reasons — to plan, to compare options, and to check that somebody else’s arithmetic is honest. This tool serves all three, and everything after the calculator explains the model instead of hiding it.
The number itself is the easy part. What takes judgement is knowing which inputs are facts in your situation and which are guesses wearing a decimal point — a distinction this page makes explicit for every field above.
It helps to separate the mechanics from the interpretation. The mechanics are fixed: BEY = (365 × d) ÷ (360 − d × t). Anyone, anywhere, entering the same inputs will get the same 5.20%. The interpretation is where experience counts: whether 5.20% is good, normal or alarming depends on comparisons covered below, and that is the part most articles about Bond Equivalent Yield never explain.
What makes a calculation page trustworthy is that its copy is derived from its own arithmetic: here bond-equivalent yield = 5.20%, recomputed every time a field changes, and the sensitivity section ranks the inputs that move the result — Discount rate on face first, at ≈10.3 % 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.
Every input in Bond Equivalent Yield, and what it does to the answer
One formula, published in full: BEY = (365 × d) ÷ (360 − d × t). Anything you can read, you can reproduce in a spreadsheet, and that reproducibility is the whole point of printing it rather than hiding it behind a button.
Discount rate on face (%) (example value 5) 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.
Days to maturity (example value 195) is a plain measured quantity — the unit shown in the label is the unit the formula expects. If the period is partial, decide whether you mean elapsed or planned time and keep that meaning across every field.
Bond Equivalent Yield with real numbers, step by step
The tool prints its own working; this is the same arithmetic on the example values, reproduced so you can follow it by hand. Starting figures: Discount rate on face (%), Days to maturity. Run to the end, the bond-equivalent yield resolves to 5.20% — This is the yield quoted on the Treasury bill screen on the bands this tool uses.
- BEY = 365 × 0.0499 ÷ (360 − 0.0499 × 195) = 5.20%
- The 360→365 switch plus price-base (not face) is the entire trick of the convention
Purchase price per $100 — 97.297 $. Read next to the headline, this is the figure that shows the shape of the trade-off.
Simple (add-on) yield over the term — 2.78 %. Read next to the headline, this is the figure that shows the shape of the trade-off.
Annualized simple yield — 5.20 %. Read next to the headline, this is the figure that shows the shape of the trade-off.
Discount vs BEY gap — 0.21 bp. Read next to the headline, this is the figure that shows the shape of the trade-off.
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.
The Bond Equivalent Yield corridor: your result across a realistic band
The honest version of any estimate is a corridor, and this one is cheap to produce: Bond Equivalent Yield was recomputed at 5 points along the dominant input, with every other field left untouched.
| Discount rate on face setting | Bond-equivalent yield |
|---|---|
| 80 % of the example value | 4.14% |
| 90 % of the example value | 4.67% |
| example inputs | 5.20% |
| 110 % of the example value | 5.74% |
| 120 % of the example value | 6.27% |
Across 5 settings of Discount rate on face, the result spans 4.14% to 6.27%. A decision that only works at one row of this table is a decision waiting for an input to move. Reproduce it in the form above by editing Discount rate on face alone; the substitution steps will follow your figures exactly.
What actually moves your Bond Equivalent Yield
Generic advice says “it depends on your inputs”; this section says exactly how much. Each field was perturbed by ±10 % in isolation and the bond-equivalent yield recomputed, so the ranking below is measured rather than asserted. For Bond Equivalent Yield 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 Discount rate on face by ±10 % and Bond Equivalent Yield lands between 4.67% and 5.74% (sensitivity ≈10.3 %)
- Days to maturity: ten percent up gives 5.21%, ten percent down gives 5.19% — ≈0.3 % of the bond-equivalent yield either way
Discount rate on face is the dominant lever here: ten percent either way moves the result by about 10.3 %, from 4.67% to 5.74%. That is where a careless figure does the most damage, so check it against a source, and treat Days to maturity 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.
Reading the result: bands, zones and thresholds
A number on its own is trivia; a number against a range is intelligence. The default case lands in the “This is the yield quoted on the Treasury bill screen” band, and bands are deliberately wide because real situations overlap. Before treating the band as fact, note its width: ten percent either way on Discount rate on face already spans 4.67% to 5.74%. 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 Bond Equivalent Yield sits next to similar measures: this tool answers “how much is the Bond Equivalent Yield”, 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.
Common mistakes with Bond Equivalent Yield (and the fix)
BEY annualizes simply, not geometrically — for maturities over one year the compounded (real) yield is slightly higher. 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.
Stopping at the first plausible answer. If the result surprises you, the productive question is which input would have to be wrong for the surprise to disappear — then go check that input.
One mistake is specific to this engine: assuming every input matters equally. The computation above shows Discount rate on face dominating — a careful figure there beats false precision everywhere else.
A final trap is presentation: reporting Bond Equivalent Yield 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.
Six things to confirm before acting on Bond Equivalent Yield
- Record the date and the inputs alongside the number so future-you knows what was assumed.
- State, in one sentence, which convention each rate, unit or period in the form is using.
- Re-verify Discount rate on face against a source document — ten percent of error there moves the headline by ≈10.3 %.
- Confirm the example values are plausible for your own situation before replacing them.
- 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.
A routine for decision-grade Bond Equivalent Yield
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 (discount rate on face (%), days to maturity). 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. Repeating a calculation with the same numbers proves only that the arithmetic is reliable — which is worth knowing.
Step 2 — compute the version you would not be embarrassed by. If a stranger audited your inputs, which set would you hand over? Enter that set, read the result, and treat everything else as upside. A figure nobody can reproduce is a figure nobody will act on twice.
Step 3 — change one input at a time. Nudge a single field by ten percent, watch the headline and its companions move, then undo it. Two or three fields will dominate — the sensitivity table above already ranks them for this engine. Precision is a promise you make about your data; make sure your inputs can keep it.
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. Write the assumptions in the same file as the result, and future arguments take minutes instead of meetings.
Step 5 — write the one-line memo. “Bond-equivalent yield = 5.20% 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. Re-running a number costs seconds; retracting a decision costs considerably more.
Who actually uses Bond Equivalent Yield — and when
In Fixed Income 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.
The companion outputs — Purchase price per $100 and Simple (add-on) yield over the term — exist for the second stage of that screen: the headline sizes the prize, while the companions describe the trade-off you are accepting to get it. A calculation you cannot explain to somebody else is a calculation you cannot defend.
There is a personal-administration use people overlook: periodic self-checking. Bond Equivalent Yield quietly drifts as life changes — rates move, bodies change, costs compound — and re-running it a few times a year catches drift while correction is still cheap. If a result feels obviously right, that is the moment to check the inputs hardest.
The questions that come up most about Bond Equivalent Yield
What affects Bond Equivalent Yield the most?
Measured on this engine, Discount rate on face is the dominant lever: moving it ±10 % shifts the bond-equivalent yield across 4.67% to 5.74% — about 10.3 % of the headline, with Days to maturity next at ≈0.3 %. The ranked list in the sensitivity section is computed live, not asserted from a template.
Which matters more: days to maturity or discount rate on face?
Discount rate on face, by a factor of about 37.0. Concretely: ten percent on Discount rate on face is worth ≈10.3 % of Bond Equivalent Yield, the same nudge on Days to maturity only ≈0.3 %. That ranking is re-computed for each page from that page’s own defaults.
What is a typical Bond Equivalent Yield?
On the worked example above Bond Equivalent Yield comes out at 5.20%. 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 Bond Equivalent Yield by hand?
Three steps: write the formula (BEY = (365 × d) ÷ (360 − d × t)), 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 Bond Equivalent Yield than any number of calculator runs.
What happens to Bond Equivalent Yield if discount rate on face changes by 10 %?
Try it in the form above and the printed substitution will follow you; the pre-computed answer for the defaults is 4.67% to 5.74% across the ten-percent probe, i.e. ≈10.3 % sensitivity on the bond-equivalent yield.
Is the Bond Equivalent Yield result of 5.20% good or bad?
Neither, on its own — the label “This is the yield quoted on the Treasury bill screen” 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 Discount rate on face alone moves it by ≈10.3 %.
Can I predict future returns with Bond Equivalent Yield?
No tool predicts; Bond Equivalent Yield computes implications. Use it to ask "if these inputs hold, what follows" — then stress the assumptions.
Can Bond Equivalent Yield be negative or empty?
Yes, and that is informative rather than broken: a negative Bond Equivalent Yield usually means the inputs encode an outflow or a shortfall, and the verdict band above labels exactly that situation instead of hiding it.
Why does the bill "yield" on my brokerage differ from the auction discount?
Your platform shows BEY or simple yield; the Treasury press release shows the discount rate. Same instrument, three numbers.
Why do 360 and 365 both appear in the formula?
Discount is earned on a 360-day money-market convention, but investors live in a 365-day year — BEY is the translation between the two calendars.
Can this tool see the numbers I type?
It cannot. There is no submission step: the calculation happens in your browser and the result disappears when you close the page. Treat the fields above as a scratchpad rather than a form.
The vocabulary of Bond Equivalent Yield
- Purchase price per $100
- 97.297 $ in the default Bond Equivalent Yield calculation — one of the secondary figures an experienced reader checks before trusting the primary number.
- Simple (add-on) yield over the term
- 2.78 % for the Bond Equivalent Yield worked case; it sits next to the main result because it carries context the headline leaves out.
- Annualized simple yield
- 5.20 % for the Bond Equivalent Yield worked case; it sits next to the main result because it carries context the headline leaves out.
- Bond-equivalent yield
- The primary output of this tool: 5.20% for the default inputs, computed exactly from BEY = (365 × d) ÷ (360 − d × t).
- Worked example
- The step-by-step substitution printed above, so the arithmetic can be re-derived by hand or in a spreadsheet.
- Verdict band
- A named zone on the range of plausible results; the example inputs land in “This is the yield quoted on the Treasury bill screen”, and your inputs may not.
- Sensitivity (±10 %)
- How far the Bond Equivalent Yield moves when a single input is nudged ten percent either way; the ranked list on this page is computed live from this engine.
The provenance of this Bond Equivalent Yield calculation
The model is published arithmetic implemented exactly as written: BEY = (365 × d) ÷ (360 − d × t). Source of record: U.S. Treasury auction conventions; SEC money-market fund BEY rules (Rule 2a-7). Specialist software layers extra coefficients on top of the same algebra; none are hidden here, and that transparency is what makes a disagreement traceable to a specific input instead of a black box.
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 sensitivity table above is part of that promise rather than a bonus: it lets you see how much of the result depends on how carefully you measured.
Next steps after the calculation
Pair this figure with the companion outputs above — the headline sizes the prize, the companions describe the risk.
Whoever you are (investors and founders comparing opportunities on equal terms), 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.