Bond Price Calculator
Enter the face value, coupon rate, yield to maturity, and maturity details to get the fair value of a bond instantly. The calculator shows clean price, dirty price, and accrued interest, plus Macaulay duration, modified duration, and convexity for interest-rate risk. Switch to reverse-solve mode to find the implied yield from a known market price. A full coupon payment schedule is included so you can see every cash flow.
Formula
Worked example
A $1,000 bond with a 5% annual coupon paid semi-annually, 10 years to maturity, and a YTM of 6%: periodic coupon C = $25, periodic rate r = 3%, n = 20 periods. PV of coupons = 25 x [1 - 1/1.03^20] / 0.03 = $371.93. PV of face = 1000 / 1.03^20 = $553.68. Clean price = $925.61.
What is a bond price?
A bond price is the present value of all future cash flows the bond will generate: periodic coupon payments plus the repayment of the face value at maturity. Because interest rates fluctuate after a bond is issued, the price at which a bond trades in the secondary market almost never equals its face value. When market yields rise above the coupon rate, the price falls below par (the bond trades at a discount) because new bonds offer better income. When yields fall below the coupon rate, the price rises above par (a premium) because the bond pays above-market income. The discount rate that makes the present value of cash flows equal the current market price is called the yield to maturity (YTM).
Clean price vs. dirty price and accrued interest
Bond prices are quoted in two ways. The clean price is the present value of future cash flows and is the figure listed in financial data services. The dirty price (also called the invoice price or full price) is the amount you actually pay at settlement: it equals the clean price plus accrued interest. Accrued interest is the fraction of the next coupon payment that has already been earned by the seller since the last coupon date. For example, if 30 days have passed since the last semi-annual coupon on a $1,000 bond paying 5%, the seller has earned 30/180 x $25 = $4.17 of the next coupon, and the buyer compensates the seller for that amount at closing. Use the "Days since last coupon" field to see the dirty price and accrued interest for your bond.
Duration and convexity: measuring interest-rate risk
Macaulay duration is the weighted average time (in years) until you receive the bond's cash flows, where each weight is the present value of that cash flow divided by the total price. It measures how long your money is "at risk." Modified duration is Macaulay duration divided by (1 + periodic yield) and approximates the percentage price change for a 1% move in yield. A modified duration of 7 years means the bond price would fall by roughly 7% if rates rose 1%. Convexity refines this estimate: because the price-yield relationship is curved (convex), duration alone understates price gains and overstates losses when rates move significantly. A higher convexity is favorable for bondholders because the bond rises more than duration predicts when yields fall, and falls less than duration predicts when yields rise.
How to use this bond price calculator
To calculate the fair value of a bond, select "Bond price (from YTM)" and enter the face value, annual coupon rate, coupon frequency, years to maturity, and the required yield. The clean price, dirty price, and all risk metrics update instantly. To find the implied yield of a bond trading at a known price, switch to "Yield to maturity (from price)" and enter the market price. The calculator solves for YTM numerically using a bisection algorithm and displays the result alongside the same risk metrics. The coupon payment schedule below the results shows every cash flow and its present value so you can verify the math period by period.
Bond price and yield relationship
| Relationship | Price | Explanation |
|---|---|---|
| Coupon > YTM | Above par (premium) | Investor pays extra for above-market income |
| Coupon = YTM | At par | Bond trades at face value |
| Coupon < YTM | Below par (discount) | Investor demands a lower price to earn market yield |
| Zero coupon | Deep discount | All return comes from capital appreciation |
How a bond price relates to par when coupon rate and market yield differ.
Frequently asked questions
Why does a bond price fall when interest rates rise?
When market interest rates rise, newly issued bonds offer higher coupons, making existing bonds with lower coupons less attractive. To compensate, the price of the existing bond must fall until its total return (including capital gain at maturity) equals the market rate. The inverse price-yield relationship is the most fundamental concept in fixed income.
What is the difference between clean price and dirty price?
The clean price is the quoted price of the bond, excluding any interest that has accrued since the last coupon date. The dirty price (invoice price) is what you actually pay: clean price plus accrued interest. Bonds are quoted clean but settle dirty, so the amount you transfer at purchase is always the dirty price.
What does yield to maturity mean?
Yield to maturity (YTM) is the internal rate of return on a bond if you hold it to maturity and reinvest all coupons at the same rate. It accounts for the purchase price, coupon payments, and the face value received at maturity, so it is the most complete single measure of a bond's return. YTM is expressed as an annualised rate.
What is Macaulay duration and why does it matter?
Macaulay duration is the weighted average time (in years) until you receive all cash flows from the bond. It is a measure of interest-rate sensitivity: a longer duration means the price is more sensitive to yield changes. A zero-coupon bond has a Macaulay duration equal to its time to maturity, while a coupon bond has a shorter duration because you receive some cash flows earlier.
How is accrued interest calculated for a bond?
Accrued interest equals the coupon per period multiplied by the fraction of the period that has elapsed since the last coupon date. Using a 30/360 day-count convention: Accrued interest = (Annual coupon / payments per year) x (Days since last coupon / Days per coupon period). The buyer pays this to the seller at settlement and then receives the full coupon on the next payment date.
What is a zero-coupon bond and how is it priced?
A zero-coupon bond makes no periodic coupon payments. Instead it is issued at a deep discount and redeems at face value. Its price is simply the present value of a single lump sum: Price = Face value / (1 + YTM)^years. To price a zero-coupon bond in this calculator, set the coupon rate to 0%.