Bond Yield Calculator
Solve yield to maturity from a bond's price or price it from a yield. Shows current yield, yield to call, accrued interest, clean vs dirty price and duration.
The interactive tool loads here when JavaScript runs.
About this toolWhat is the Bond Yield Calculator?
This bond yield calculator works in both directions. Give it a bond's face value, coupon rate, years to maturity and coupon frequency plus a yield, and it returns the price; give it a market price and it solves the yield to maturity. Alongside it shows the current yield, the accrued interest and the gap between the clean and dirty price, Macaulay and modified duration, convexity, and the price change for a one-point move in yields.
For callable bonds, switch on the call option and enter the call date and price to get the yield to call and the yield to worst. A price-yield curve shows where the bond sits and why price falls faster than linearly as yields rise.
- Price from yield and yield to maturity from price
- Current yield, yield to call and yield to worst
- Clean price, dirty price and accrued interest between coupon dates
- Macaulay and modified duration with convexity
- Price-yield curve and a full cash-flow table
How to use the Bond Yield Calculator
- Choose Price from yield or Yield from price.
- Enter the face value, the annual coupon rate, the years to maturity and the coupon frequency.
- Enter the yield to maturity, or the market price and whether it is clean or dirty.
- For a callable bond, switch on the call option and enter the years to the first call and the call price.
- Read the price or yield, current yield, accrued interest, durations and the price-yield curve.
Worked examples
Discount bond
Input
$1,000 face, 5% coupon, semiannual, 10 years, 6% yield
Output
Price $925.61; current yield 5.402%; Macaulay duration 7.895 years; modified 7.665
The bond trades below par because its coupon is below the market yield. If yields rise one point the full price falls to $857.88, and if they fall one point it rises to $1,000.
Yield from a premium price
Input
Same bond priced at $1,100, callable in 5 years at $1,020
Output
Yield to maturity 3.789%; yield to call 3.192%
At a premium the issuer is likely to call when rates are low, so the yield to call (the lower of the two, the yield to worst) is the realistic figure.
Between coupon dates
Input
Same bond with 9.75 years left, 6% yield
Output
Clean price $926.89; dirty price $939.39; accrued interest $12.50
Half a coupon period has passed since the last payment, so the buyer owes the seller half of the $25 semiannual coupon on top of the quoted price.
Background and insight
A bond's price is the present value of its remaining coupons and principal, discounted at the yield. US markets quote yields on a bond-equivalent basis: an annual rate that compounds at the coupon frequency, so a 6% yield on a semiannual bond means 3% per half-year. A 10-year bond with a 5% semiannual coupon priced at a 6% yield is worth $925.61 per $1,000 of face value, a standard textbook example that the calculator's tests reproduce.
There is no formula for yield given price, so the calculator solves for it numerically with Newton's method inside a bisection bracket, to a precision far below a basis point. Current yield (annual coupon ÷ price) is simpler but ignores the pull to par: a discount bond earns more than its current yield because it is redeemed at face value.
Between coupon dates the seller is owed the interest accrued since the last coupon. Quotes are clean prices; the buyer pays the dirty (invoice) price, which adds accrued interest. Enter a maturity such as 9.75 years and the calculator places you half-way through a semiannual period, computes accrued interest and reports both prices. It approximates the day count by the fraction of the period, close to 30/360; Treasuries use actual/actual, so settle real trades from the bond's own conventions.
Macaulay duration is the present-value-weighted average time to the cash flows; modified duration divides it by (1 + yield per period) and gives the approximate percentage price change for a one-point change in yield. A 5-year 10% annual-coupon bond at a 10% yield has a Macaulay duration of 4.1699 years and modified duration of 3.7908.
Common use cases
Comparing bonds
Turn quoted prices into yields to maturity so bonds with different coupons and maturities can be compared.
Checking interest-rate risk
Use modified duration to estimate how much a bond or ladder would lose if rates rose.
Callable bond analysis
See whether yield to call or yield to maturity is the yield you are really likely to earn.
CFA and finance coursework
Check bond pricing, YTM, duration and convexity problems with every cash flow listed.
Tips and limitations
- Yield to maturity assumes coupons are reinvested at the same yield and the bond is held to maturity without default.
- Compare yields on the same basis. A semiannual bond-equivalent yield is not the same as an annual effective yield.
- Duration is a linear approximation. For large rate moves, convexity makes the real price change kinder than duration predicts.
- Tax-exempt municipal bonds and inflation-linked bonds need a tax-equivalent or real-yield comparison that this calculator does not do.
Frequently asked questions
How do you calculate yield to maturity?
YTM is the discount rate that makes the present value of all remaining coupons and the principal equal the bond's price. It has no closed-form solution, so it is found by trial and error or a numerical solver. This calculator uses Newton's method with a bisection fallback.
What is the difference between current yield and yield to maturity?
Current yield is the annual coupon divided by the price and ignores the gain or loss to par at maturity. YTM includes it. A bond bought at a discount has a YTM above its current yield; one bought at a premium has a YTM below it.
Why do bond prices fall when interest rates rise?
A bond's coupons are fixed, so when new bonds pay higher yields, an existing bond must sell for less to offer a buyer the same yield. The longer the bond's duration, the bigger the price drop for a given rise in rates.
What is the difference between clean and dirty bond prices?
The clean price excludes interest that has accrued since the last coupon; the dirty price includes it. Prices are quoted clean, but the buyer pays the dirty price and receives the full next coupon.
What does modified duration tell you?
The approximate percentage change in price for a one-point change in yield. A modified duration of 7.67 means a 1% rise in yields cuts the price by roughly 7.67%, before the small correction from convexity.
What is yield to call?
The yield you would earn if the issuer redeems the bond at its call price on the call date. For bonds trading at a premium it is usually lower than yield to maturity, and the lower of the two is called yield to worst.
Is there an in-depth guide to the Bond Yield Calculator?
Yes. “APY, Bond Yields and SIP Returns: Reading the Rate Correctly” covers the background, how it works, common pitfalls and worked examples. Read the full guide.
Related Tools You May Like
Free, in-browser tools that pair well with this one.