Bond Price Calculator
The price of a bond is the present value of all its future cash flows: the periodic coupon payments and the face value returned at maturity. When the market yield (also called required rate of return) differs from the coupon rate, the bond trades at a discount or premium to face value. This bond price calculator uses the standard fixed-income present value formula to compute the fair price given the face value, coupon rate, market yield, years to maturity, and payment frequency. Understanding bond pricing helps fixed-income investors assess whether a bond is cheap or expensive relative to current market rates, compare bonds with different coupons and maturities, and calculate the capital gain or loss if they plan to sell before maturity. Enter your bond parameters below to see the calculated clean price, total coupon income, and capital gain or loss at maturity.
Bond price formula
Price = C x [1 - (1 + r)^(-n)] / r + F / (1 + r)^n
Where: C = periodic coupon = (Face x Annual Rate) / freq
r = periodic yield = Annual Yield / freq
n = total periods = Years x freq
F = Face value
The first term is the present value of the coupon annuity; the second term is the present value of the face value repaid at maturity.
Bond pricing relationships
- When yield equals coupon rate, bond price equals face value (par bond).
- When yield is greater than coupon rate, bond price is below face value (discount bond).
- When yield is less than coupon rate, bond price is above face value (premium bond).
- Longer-maturity bonds are more price-sensitive to yield changes than shorter-maturity bonds.
- Lower coupon bonds have greater price sensitivity (duration) than higher coupon bonds with the same maturity.
Bond pricing: frequently asked questions
Why does a bond price change when interest rates change?
Bond prices and interest rates move in opposite directions. When market interest rates rise above a bond's coupon rate, the bond becomes less attractive, so its price falls below face value (it trades at a discount). When rates fall below the coupon rate, the bond pays above-market income, so its price rises above face value (it trades at a premium).
What is the difference between face value and price?
Face value (also called par value) is the amount repaid at maturity, typically $1,000. The price is what you pay in the market today. A bond priced at $950 trades at a discount; one priced at $1,050 trades at a premium. At maturity, the issuer always pays the face value regardless of the market price.
What coupon payment frequency should I use?
Most US Treasury bonds and corporate bonds pay interest semi-annually (twice per year). Some bonds pay annually, monthly, or quarterly. The calculator adjusts the periodic rate and number of periods based on your selected frequency. When in doubt, use semi-annual for US bonds.
What is accrued interest?
If you buy a bond between coupon dates, you owe the seller accrued interest for the days since the last coupon. The dirty price (what you actually pay) equals the clean price (what this calculator shows) plus accrued interest. Most bond quotes show the clean price.
How accurate is the bond price formula?
The standard present value formula used here is exact for bullet bonds (fixed coupon, single maturity) with no embedded options. It assumes all cash flows are discounted at the same market yield. Callable, puttable, or floating-rate bonds require more complex models.
Official sources
- U.S. Treasury: Treasury Securities Auction Information.
- SEC Office of Investor Education: Bonds - An Introduction to Bond Basics.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.