Bond Yield, Price & Spread.
The fixed-income desk view.
A bond calculator solves the three things a fixed-income trader needs: yield to maturity from a price, price from a target yield, and spread to a Treasury benchmark — plus modified duration and convexity for risk sizing.
Bonds are priced as the present value of their cash flows discounted at a single rate. Given any three of {price, yield, coupon, maturity} this calculator solves for the fourth, then computes the spread to your Treasury benchmark in basis points and the duration / convexity / DV01 numbers a desk uses to size a hedge. Plain-vanilla bullet bonds only — for callable structures, see the FAQ.
How We Calculate This
Price from yield (closed-form)
where P is price, C is the per-period coupon (face × annual coupon ÷ frequency), r is the per-period yield (annual yield ÷ frequency), n is the total number of coupon periods, and F is face value.
Yield from price (numerical)
Solved by bisection on the price function above. Price is monotonically decreasing in yield, so bisection converges reliably; we bracket [−50%, 200%] which handles distressed and zero-coupon edge cases.
Modified duration
Convexity
DV01
Spread
This is a Treasury nominal spread, not a Z-spread or OAS. For non-callable bonds against an on-the-run Treasury benchmark, the three give very similar values; for callable bonds the OAS adds a callable-option correction this calculator does not model.
Sources
Fabozzi, Fixed Income Analysis (CFA Institute Investment Series); SIFMA Standard Bond Conventions; U.S. Treasury Daily Yield Curve for benchmark rates.
How to Use the Bond Calculator
Start with the bond's specification: face value, coupon, years to maturity, and payment frequency. US corporate and Treasury bonds pay semi-annually; agency notes are usually semi-annual; some sovereigns pay annually. Match the calculator to the specific bond's prospectus.
Choose your mode. Yield from price is what a trader does when a quote comes in: "Treasury 4.5s of '34 at 99-08 — what's the yield?" Plug in the price and the YTM falls out by bisection. Price from yield is the reverse: "I want to bid this bond at 6.25% — what's that in dollars?" Both modes produce the full risk-metric panel.
The Treasury benchmark input drives the spread output. Use a Treasury of comparable maturity — for a 10-year corporate bond, plug in the 10-year on-the-run Treasury yield from the Treasury Daily Yield Curve. The resulting spread to Treasury, expressed in basis points, is how the bond market actually talks about pricing: "trading 145 over the 10-year."
The Math, In One Sentence
A bond's price is the present value of its coupon stream and face-value redemption, discounted at a single rate (the yield). If the discount rate equals the coupon rate, price equals face value. If the discount rate is higher than the coupon, the bond trades at a discount (price below par). If the discount rate is lower than the coupon, the bond trades at a premium (price above par). That's the entire framework — every other fixed-income metric, including the ones in the results panel above, is a derivative or transformation of this single equation.
What the Risk Metrics Tell You
Modified duration is the percentage price change for a 100bp shift in yield. A bond with modified duration of 7 will gain roughly 7% if yields fall 100bps. The approximation is linear; for large yield moves, you need convexity to correct it.
Convexity is the curvature of the price-yield relationship. Higher convexity is good for the bondholder — it means the bond gains more when yields fall than it loses when yields rise. For two bonds with identical duration, the one with higher convexity is the better defensive holding into a volatile environment.
DV01 ("dollar value of an 01") translates duration into a dollar number: how much a bond's price moves for a 1-basis-point change in yield. It's what fixed-income desks use to size hedges — if your portfolio has $50,000 of DV01 exposure, you can offset it with a Treasury futures position of equivalent DV01.
Spreads in Practice
The spread output is the language of corporate-bond trading. A "T+150" quote means "150 basis points over the comparable-maturity Treasury." When credit conditions deteriorate, spreads widen across the market — high-yield spreads can blow out from 350bps to 700bps in weeks during a recession. When conditions improve, they compress back. Tracking spreads over time is how credit traders measure the cost of borrowing for a given issuer relative to risk-free, with the macro rate environment stripped out.
For investment-grade (BBB-, BBB, BBB+, A-, A, A+, AA, AAA) corporate bonds, typical spread ranges in normal markets: AAA 30–80bps, AA 50–120bps, A 80–180bps, BBB 130–250bps. For high-yield: BB 250–450bps, B 400–700bps, CCC 800bps+. These are heuristics — actual spreads vary by sector, maturity, and current market regime. The ICE BofA US Corporate Index on FRED is the standard benchmark for IG spreads; the BofA US High Yield Index is the benchmark for HY.
Limitations
- Bullet bonds only. Callable, putable, and convertible bonds require option-adjusted spread (OAS) calculations that aren't modeled here. For Treasuries and most non-callable IG corporates, the bullet model is accurate.
- Whole coupon periods. The model assumes you're at a coupon date. Between dates, actual settlement pricing includes accrued interest (the clean-vs-dirty price distinction) that this calculator doesn't compute.
- Single yield curve. Real spread analysis uses the full Treasury curve interpolated to the bond's exact maturity (Z-spread). The single-point benchmark here is a simplification — accurate for matched-maturity bonds, less so for off-the-run maturities.
- No credit modeling. The spread shown is what the market is currently pricing; it doesn't predict defaults or recommend a fair-value spread for a given rating. Compare to sector index spreads from FRED if you want a relative-value reference.
Related Tools and Reading
- Business Loan Calculator — the same APR-with-fees math, applied to private-market lending.
- FCCR Calculator — credit-side analog: how the issuer's underlying covenants are tested.
- Global Cash Flow Calculator — the obligor's repayment capacity, on the credit side of capital markets.
- Caldridge methodology — full formula citations for every calculator.
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Open toolFrequently Asked Questions
What is yield to maturity (YTM)?
YTM is the single discount rate that makes the present value of all future bond cash flows equal to the bond's current market price. It is the bond's internal rate of return if held to maturity and assuming all coupons are reinvested at YTM.
What does spread to Treasury mean?
Spread to Treasury is the difference between a bond's yield and the yield of a Treasury security of comparable maturity, expressed in basis points (bps). It is the market's compensation for the credit risk, liquidity risk, and other risk factors that distinguish the bond from a risk-free government issue.
What is modified duration?
Modified duration measures the percentage change in a bond's price for a 1% (100bp) change in yield. A modified duration of 7 means the bond will lose roughly 7% of its value if yields rise 100bps, or gain 7% if yields fall 100bps.
What is DV01?
DV01 (dollar value of an 01) is the dollar change in a bond's price for a 1-basis-point change in yield. Fixed-income desks use DV01 to size hedges — if a bond has a DV01 of $0.85, you need 85 cents worth of duration offset per basis point.
How is convexity used?
Convexity is the second derivative of price with respect to yield. Duration alone gives a linear approximation; convexity corrects for the curvature, meaning the actual price gain when yields fall is larger than duration predicts, and the actual loss when yields rise is smaller. The price change estimate including convexity is: −ModDur × dy + 0.5 × Convexity × dy².
Does this calculator handle callable bonds?
No — this is a plain-vanilla bullet bond calculator only. Callable bonds require yield-to-call and yield-to-worst calculations that depend on the bond's specific call schedule. For non-callable Treasuries, agencies, and most investment-grade corporate bonds, this calculator works.
What is a typical spread for an investment-grade corporate bond?
Investment-grade (BBB and above) corporate bond spreads to Treasuries typically range from 80 to 200 basis points in normal market conditions, depending on rating, sector, and maturity. High-yield bonds (below BBB) typically trade at 300–600+ bps over Treasuries; distressed bonds can trade at 1,000bps+.
Clean price vs. dirty price — which does this calculator show?
This calculator shows the clean price: the present value of remaining coupons and face, assuming you're standing at a coupon-payment date. Between coupon dates the bond also has accrued interest, and the actual settlement price (the dirty price) equals clean price plus accrued. Bond quotes in the U.S. market are conventionally clean; settlement is dirty.
Why does YTM assume reinvestment at the same rate?
The math behind YTM equates the bond's price to the present value of cash flows discounted at a single rate. That single rate implicitly assumes every coupon you receive is reinvested at that same YTM until maturity. In practice, reinvestment happens at whatever the market rate is when each coupon arrives — so the realized yield can differ from the quoted YTM. The longer the maturity and the higher the coupon, the more reinvestment risk matters.
What should I use instead for callable bonds?
For a callable bond, the issuer can buy it back at preset call dates. The market-relevant yield is yield-to-worst (YTW) — the minimum of YTM and yield-to-call across every call date. To price callable bonds properly you also want option-adjusted spread (OAS) instead of nominal spread. Bloomberg's YA function, the QuantLib open-source library, and most fixed-income platforms handle this; a plain bullet model like this one over-estimates yield because it ignores the call option's negative convexity.