How to use it
- Choose What to calculate: the price from a yield, or the yield from a price.
- Enter the face value, the coupon rate and how many times a year the coupon is paid.
- Enter the last coupon date, the settlement date and the maturity date. The maturity date must fall on the coupon schedule.
- Enter the yield or the clean price, then read the price, the accrued interest and the durations below.
How the price and the yield are calculated
A bond pays a coupon of face value × coupon rate ÷ coupons a year at each coupon date, and the face value at maturity. Its price is the present value of those payments, discounted at the yield for one period from the settlement date. The price paid includes the interest built up since the last coupon; the quoted clean price leaves it out.
With N payments left, the k-th one falls k − α periods after settlement, where α is the part of the current period already passed. The dirty price is the sum of the payments discounted at (1 + y ÷ m) to the power of minus the time. The yield to maturity is the rate that makes that sum equal the clean price plus the accrued interest. It has no formula for a coupon bond, so Newton's method finds it.
P_dirty = Σ CF_k ÷ (1 + y ÷ m)^(k − α)
AI = C × α
P_clean = P_dirty − AI
C coupon per period = face value × coupon rate ÷ m
m coupons a year
α share of the current period already passed
y yield to maturity, nominal and a yearAccrued interest and the day count
The accrued interest is the coupon multiplied by the share of the period that has passed, and that share depends on how the days are counted. In 30/360 every month has 30 days and the year 360, so α = days ÷ (360 ÷ m). In actual/actual (ICMA) it is the real days since the last coupon ÷ the real days in the period.
- 30/360 (US) counts the 31st as the 30th. It is used for US corporate bonds and many US agency issues. The end-of-February rules for bonds that pay on the last day of the month are not applied here.
- Actual/Actual (ICMA) is used for US Treasury bonds and notes, and gives every day of the period the same value.
Duration
The Macaulay duration is the present-value-weighted average time to the payments, in years. The modified duration divides it by (1 + y ÷ m). It is the approximate percentage fall in price for a rise of one percentage point in yield, and is accurate for small changes.
What this calculator does not include
- Taxes on the coupons or on any gain when the bond is sold.
- Brokerage, custody fees, and the bond's own terms such as a call option, which change the payments.
- Inflation-linked or floating coupons: the coupon here is fixed.
Worked example: 1,000 face value, 5% coupon paid twice a year, 6% yield
The coupon is 1,000 × 5% ÷ 2 = 25 every six months. The settlement date, 10 November 2026, is 55 days into the period that began on 15 September, and 30/360 counts the period as 180 days, so α = 55 ÷ 180 = 0.3056 and the accrued interest is 25 × 0.3056 = 7.64.
Ten payments are left: nine coupons of 25 and the last coupon with the 1,000 repaid. Discounted at 3% per half-year, they give a dirty price of 966.03 (966.0348 before rounding). Taking off the accrued interest gives a clean price of 958.40, the current yield is 50 ÷ 958.40 = 5.22%, and the durations are 4.3189 years (Macaulay) and 4.1931 years (modified).
| Figure | Value |
|---|---|
| Accrued interest | 7.64 |
| Dirty price (amount paid) | 966.03 |
| Clean price | 958.40 |
| Macaulay duration | 4.3189 years |
| Modified duration | 4.1931 years |
Frequently asked questions
What is the difference between the clean price and the dirty price?
The dirty price is what the buyer pays: the clean price plus the interest built up since the last coupon. Prices are usually quoted clean, so the accrued interest is added when the bond settles.
Why does the price fall when the yield rises?
The payments are fixed, so a higher yield discounts each one more and it is worth less today. When the yield equals the coupon rate, a bond priced on a coupon date sells at its face value.
What is the difference between 30/360 and actual/actual?
30/360 counts every month as 30 days and the year as 360, while actual/actual counts the real days in the coupon period. The accrued interest therefore differs slightly between US corporate bonds, which usually use 30/360, and US Treasury notes, which use actual/actual.
Does the yield to maturity show what I will earn?
Only if you hold the bond to maturity, receive every coupon on time, and reinvest each coupon at the same yield. Reinvestment rates change, so the return you actually get can differ.
What does the modified duration tell me?
It estimates how much the price moves when the yield moves. A modified duration of 4.19 means a price fall of about 4.19% for a one-point rise in yield, which is only an approximation for large changes.
Are the figures I enter sent to a server?
No. The calculation runs in your browser, and nothing you enter is sent to us.
Sources
- Wikipedia: Bond valuation (present value, clean and dirty price)
- Wikipedia: Yield to maturity (zero-coupon formula, coupon bonds, current yield)
- Wikipedia: Duration (finance) (Macaulay and modified duration)
- Wikipedia: Day count convention (30/360 US and actual/actual ICMA)
Figures and text last checked on Tuesday, November 10, 2026.