Investment & Planning

Bond Yield Calculator

Free bond yield calculator for investors and analysts: solve yield to maturity and yield to call from price, price a bond from a target yield, and report current yield, accrued interest, duration, convexity, and the cash-flow schedule.

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What is Bond Yield Calculator?

Yield is the price of a bond read backwards, and this calculator runs that reading in three directions: it solves yield to maturity and yield to call from a market price, prices a bond from a target yield, and measures the interest-rate risk of either answer with duration, convexity, and price value of a basis point. Open it on the defaults — a 1,000-face 4.25% coupon bond with ten years left, quoted at 987.50 — and the solver returns a 4.41% yield to maturity against a 4.30% current yield: the 1.25% gap between price and par is recovered on top of the coupons. Flip to price mode and the same machinery runs forwards, with a 4.5% target yield pricing the bond at 980.05. Every mode reports the same supporting cast — classification as premium, discount, or par; accrued interest and the dirty price when you supply day counts; the full cash-flow schedule; and a price–yield curve that draws the convex shape the word convexity is named after. Callable bonds get their own reading: the corporate preset prices at 1,012 and returns a 5.22% yield to maturity but a 5.06% yield to call, with a call-risk note attached.

When to Use This Calculator

  • Before buying any bond on the secondary market, to see what the quote really yields.
  • When a callable bond trades above par and the call could cut the holding period short.
  • At portfolio review, to convert an expected yield shift into an expected price move.
  • On settlement date, to verify accrued interest and the dirty price.
  • When pricing a new issue against prevailing market yields.
  • For coursework and exam prep on bond math, duration, and convexity.

Steps:

  1. Choose a mode: yield solves returns from a price, price solves a price from a yield, and duration reports rate risk for either.
  2. Enter the face value — 1,000 is the market standard, but any positive par works.
  3. Set the coupon rate and payment frequency; annual, semiannual, quarterly, and monthly are all supported.
  4. Enter years to maturity, using decimals for a bond part-way through its life.
  5. Supply the clean price in yield mode, or the target yield in price mode.
  6. Optionally add call terms to compute yield to call, and day counts to accrue interest toward a settlement date.
  7. Read the hero result, then the breakdown: classification, current yield, accrued interest, and yield to call when priced.
  8. Use the schedule and the price–yield chart below to see when cash arrives and how price moves with yield.

Formula

P = C × (1 − (1 + r)^−n) ÷ r + F ÷ (1 + r)^n r = y ÷ k, n = T × k C = face × coupon ÷ k (payment per period) Current yield = annual coupon ÷ price YTM solves P for y by bisection; negative yields allowed Dirty price = clean price + accrued; accrued = C × days since ÷ days in period D_mod = D_mac ÷ (1 + y ÷ k); BPV = D_mod × P × 0.0001 Price classification: P > F premium, P < F discount, P = F par

Use Cases

  • Check the yield a broker's quote actually delivers before buying on the secondary market.
  • Price a new bond issue from the yield the syndicate is marketing.
  • Compare a callable corporate's yield to call against its yield to maturity before accepting the premium.
  • Size interest-rate risk for a portfolio position: modified duration and BPV translate yield moves into price moves.
  • Verify accrued interest at settlement so the invoice price matches the dealer's.
  • Study for finance coursework: see the same bond priced three ways from one set of inputs.

Key Benefits

  • Three bond questions — yield, price, and risk — in one instrument with shared inputs.
  • True yield-to-call for callables, plus a call-risk flag whenever the price sits above the call price.
  • Accrued interest and dirty price from your own day counts, so settlement math matches the dealer's.
  • Duration, convexity, and BPV together: the linear estimate, the curvature correction, and the per-basis-point price.
  • Full cash-flow schedule and price–yield curve for every solved state.
  • Free to use, with export and print for records, reports, or coursework.

Pro Tips

  • Match the frequency to the bond's actual schedule — US Treasuries and most corporates pay semiannual.
  • Always check yield to call on anything priced above its call price; the issuer's option caps your return.
  • Use BPV for small moves and the price–yield chart for large ones: duration linearizes, convexity bends.
  • Quote clean, settle dirty: add accrued interest yourself whenever you enter day counts.
  • Compare the coupon with the solved yield: coupon above yield means a premium, below means a discount.
  • Current yield sits between the coupon rate and yield to maturity whenever a bond trades away from par.

Common Mistakes to Avoid

  • Treating current yield as the return: it excludes the 1.25% discount to par the holder also earns on the defaults.
  • Comparing callable yields at maturity only: the corporate preset yields 5.22% to maturity but 5.06% to call.
  • Forgetting accrued interest at settlement: the clean price is quoted, the dirty price is paid.
  • Mixing frequencies: the same 4.41% yield prices the default bond at 987.50 semiannually but 987.61 annually.
  • Reading duration as a calendar horizon: modified duration is a percentage sensitivity, not the years to maturity.
  • Ignoring price limits: a yield cannot be solved outside -99% to 100%, and prices beyond the cash flows have no finite solution.

Key Terms Explained

Yield to maturity:
the annual return that discounts every remaining cash flow back to the current price — 4.41% on the defaults.
Current yield:
annual coupon divided by price — 4.30% here — with no regard for the pull to par.
Yield to call:
the same solve stopped at the call date and call price — 5.06% on the corporate preset versus 5.22% to maturity.
Clean price:
the quoted price excluding accrued interest — 987.50 on the defaults.
Accrued interest:
the seller's share of the next coupon — 10.68 after 91 of a 181-day period on a 4.25% semiannual bond.
Modified duration:
the percentage price change per unit of yield — 8.06 here, so about 8.06 per 100 basis points.
Convexity:
the curvature duration ignores — 77.3 on the defaults, worth 3.69 of price at a 100 basis point move.
Price value of a basis point:
the dollar price change for a one basis point yield shift — 0.80 on the defaults.

Related Concepts

Example

Take the page as it opens: a 1,000-face bond, a 4.25% coupon paid twice a year, ten years to maturity, quoted at 987.50. The current yield is the easy part — 42.50 of annual coupon over 987.50 is 4.30% — but the yield to maturity also has to recover the 12.50 discount to par, so the solver lands at 4.41%. Because the price sits below face, the bond is classified as a discount. Switch to price mode and ask the reverse question: what does a 4.5% target yield cost? 980.05, a 19.95 loss against face. Switch to duration mode on the original price and the risk reading appears: Macaulay duration 8.24 years, modified duration 8.06, so a 100 basis-point rise in yield implies about 79.58 of price loss — 0.80 per basis point — with convexity of 77.3 softening the actual loss on a full reprice to 75.89. Enter 91 days since the last coupon of a 181-day period and accrued interest of 10.68 joins the clean price to make the 998.18 dirty price you would actually settle.

Interpreting Your Results

Read the page left to right, top to bottom. The mode tabs choose the direction — yield, price, or duration — and the preset chips load complete bond scenarios: a ten-year Treasury-style discount, a callable corporate, a short discount issue, and a zero-coupon. The terms card sets face, coupon, frequency, and term; the advanced card adds call terms and accrual days. The hero reports the solved number with its classification, and the sub-stats break it into current yield, accrued interest, dirty price, and yield to call when call terms exist. Below, the result breakdown repeats every figure with its label, the schedule lists each cash flow discounted to present value, and the price–yield curve draws the convex relationship directly. The step-by-step panel walks the arithmetic in the same order, and the sensitivity grid answers what-if questions across terms and yields. Red warnings block results until the inputs are valid; amber notes are advisory and never stop the solve.

Frequently Asked Questions

What is yield to maturity?
Yield to maturity is the annual return a bond pays if you hold it to its final date at the current market price. It folds together three things: the coupon stream, the timing of every payment, and the gap between what you pay and the face value you receive. On this page's defaults — a 1,000 face, 4.25% semiannual coupon, ten years remaining, quoted at 987.50 — the current yield alone is 4.30%, but the solver returns 4.41% to maturity because the buyer also recovers the 12.50 discount to par over the remaining term. The calculator solves it by bisection: it searches for the periodic rate whose discounted cash flows equal the price, then annualizes. Negative yields are allowed down to -99%, so even a bond bought above its undiscounted cash flows produces a truthful, if negative, answer.
How is yield to maturity different from current yield?
Current yield is the simplest reading: the annual coupon divided by the price, ignoring everything that happens between today and maturity. On the defaults that is 42.50 divided by 987.50, or 4.30%. Yield to maturity adds the pull to par — the 12.50 an investor gains as the price converges on the 1,000 face at maturity — plus the timing of every payment. The two readings diverge most on bonds far from par: a deep discount bought at 850 yields 6.29% to maturity while its current yield on a 4.25% coupon is only 5.00%. On premium bonds the ordering flips: a bond priced at 1,012 with a 5.5% coupon shows a 5.43% current yield but just 5.22% to maturity, because the premium given up at maturity reduces the return. Current yield is a snapshot; yield to maturity is the whole film.
What is yield to call and when should I use it?
Yield to call answers the same pricing question but stops the clock at the first date the issuer may redeem, at the call price instead of par. It matters whenever a bond trades above its call price, because an issuer facing lower rates will refinance and cut your high-coupon stream short. Load the callable corporate preset: a 5.5% coupon bond five years from maturity, priced at 1,012, solves to a 5.22% yield to maturity — but called at par in year three it delivers only 5.06% to call, and the calculator raises a call-risk note because the market price sits above the 1,000 call price. When yield to call falls below yield to maturity, the call is the binding constraint and the lower figure is the honest expectation for a premium callable bond.
Why do bond prices and yields move in opposite directions?
Because a bond's cash flows are fixed at issuance, the only variable left to adjust is the price. When required yields rise, newly issued bonds pay more, so an existing bond with smaller coupons must trade below par to offer a comparable return — its price falls until the discounted value of its fixed flows matches the market. Reverse the move and the price climbs. The calculator shows both directions directly: price the default bond at a 3.65% yield and it costs 1,050, a 5.00% premium to par; price it at 6.29% and it costs only 850, a 15.00% discount. The price–yield curve below the result draws the relationship — always downward sloping and convex, so prices rise faster when yields fall than they fall when yields rise by the same amount.
What do premium, discount, and par mean?
They describe where the market price sits relative to the face value the bond repays. At par the price equals face — as in the corporate inputs run at a 5.5% coupon and a 5.5% yield, which price at exactly 1,000.00. A premium bond trades above face: priced at 1,050 it sits 5.00% above par, which happens when its coupon beats what current markets require, so buyers pay extra for the richer stream. A discount bond trades below face: at 850 it sits 15.00% below par, compensating buyers with a capital gain alongside the smaller coupons. The classification row in the result breakdown reports which case you are in, and the premium or discount figure is measured against face value, not against your purchase price.
How does accrued interest work?
Coupons are paid in arrears, but interest accrues every day between payment dates. Whoever holds the bond on the payment date earns it, so a buyer between coupons pays the seller compensation — the accrued interest — on top of the quoted clean price. That total is the dirty price, the amount that actually settles. Set days since last coupon to 91 of a 181-day period on the default 4.25% semiannual bond and the accrual is 21.25 times 91 divided by 181, or 10.68, turning the 987.50 quote into a 998.18 settlement. With no day counts supplied the calculator reports zero accrual and a dirty price equal to the clean price, which is exactly right on a coupon date itself.
What does duration tell me about rate risk?
Duration converts a yield move into an expected price move. Macaulay duration is the present-value-weighted average time to the bond's cash flows — 8.24 years on the defaults, less than the ten-year term because the coupons arrive first. Modified duration divides that figure by the periodic yield factor and becomes a sensitivity: 8.06 here means the price changes about 8.06% for every 100 basis points of yield, or 79.58 on a 987.50 price, and the result panel also reports the same reading per single basis point as 0.80. The sensitivity grid repeats the measure across terms and yields, and the long end shows why it matters most there: a 30-year bond at par carries a modified duration near 22.5, so the same 100 basis point move costs roughly 224.78.
What is convexity and why does it matter?
Duration is a straight-line estimate of a curved relationship, and convexity is the curve. The default bond's modified duration of 8.06 predicts a 79.58 loss when yields rise 100 basis points, but repricing the cash flows exactly at the higher yield gives 911.61 — a fall of only 75.89. The 3.69 difference is convexity working in the holder's favour: prices fall less than the line predicts when yields rise, and rise more than the line predicts when yields fall. The figure of 77.3 on the defaults measures that curvature, and it grows as the term lengthens or the coupon shrinks — the 30-year 2% par bond reports 612.8, roughly eight times the curvature of the ten-year default, which is why long, low-coupon bonds reward convexity-aware pricing so heavily.
Does payment frequency change the bond's price?
Yes, when you hold the annual yield constant, because compounding changes with it. The same 4.25% ten-year bond at a 4.41% annual yield prices at 987.50 when coupons arrive semiannually and 987.61 when they arrive once a year — small, but the convention must match how the bond actually pays or the quote is wrong by more than rounding. Real-world conventions are stable: US Treasuries and most corporates pay semiannual, many European and Australian bonds pay annual, and some money-market instruments pay monthly or quarterly. Select the schedule on the terms card; the calculator divides the yield by that frequency for the periodic rate and multiplies the term to count the periods.
Can a bond have a negative yield?
Yes — when the price exceeds the sum of the cash flows valued at a zero discount rate, no positive rate can bridge the gap and the solved yield falls below zero. That happened across Europe and Japan for much of the past decade, and it occurs for an individual bond whenever a flight-to-quality rally pushes the price above every coupon the bond will ever pay. The calculator allows yields down to -99%, so entering a price above the undiscounted cash flows returns a negative yield to maturity rather than an error. The practical reading is simple: you are certain to receive less in total than you paid, the nominal loss is locked in at purchase, and the negative yield merely expresses that loss as an annual rate.
How are zero-coupon bonds priced?
There are no coupons to discount, so the entire return is the gap between a deep discount price and the face value repaid at maturity. Set the coupon to 0 — or load the zero-coupon preset — and a 10-year bond priced at 620 solves to a 4.84% yield to maturity while its current yield is exactly 0.00%, since there is no coupon to divide. The classification shows the full 38.00% discount to par. Zero-coupon bonds also carry the maximum duration for their term: with no intermediate payments every dollar arrives at maturity, so the Macaulay duration equals the full 10 years and the modified duration is 9.76 — higher than the 8.06 of the coupon-paying default, which is exactly why zeros swing hardest when rates move.

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