---
title: "Bond Price Calculator with Duration | Coupon Beacon"
description: "Price a bond from its yield: clean and dirty price, accrued interest, premium or discount, Macaulay and modified duration, convexity and DV01."
url: https://couponbeacon.bond/bond-price-calculator/
---

# Bond price calculator

Turn a yield into a price. Enter the yield to maturity, coupon and term to get the clean and dirty price, then see how sensitive that price is to interest rates.

Clean price per 100

96.103

$961.03 for $1,000 face at a 5.000% yield, compounded semiannually.

Settles on a coupon date, so no interest has accrued.

### Interest-rate sensitivity

Clean price per 100 Duration estimate

| Change | Actual | Duration only | + convexity |
| --- | --- | --- | --- |
| Yield −1 point (4.00%) | 104.088 | 103.713 | 104.075 |
| Yield +1 point (6.00%) | 88.842 | 88.492 | 88.854 |

## Pricing a bond from its yield

Each remaining coupon and the face value are discounted at the yield per period and added up. That total is the dirty price; take away the accrued interest and you have the clean price bonds are quoted at. A yield above the coupon rate prices the bond at a discount to face value, and a yield below it at a premium.

### Duration and convexity

Macaulay duration is the present-value-weighted average time to the bond's cash flows, an idea Frederick Macaulay set out in 1938. Modified duration divides it by (1 + y/f) and approximates the percentage price change for a one-point move in yield. Convexity measures the bend in the curve: the dashed duration line sits below it, so adding convexity brings the estimate closer. DV01 is the dollar change for a 0.01% move.

% price change ≈ − modified duration × Δy + ½ × convexity × (Δy)²

Example: at a 5% yield, a 10-year bond with a 4.5% semiannual coupon is worth 96.103 per 100. With a modified duration of 7.919, a rise to 6% should cost about 7.9%; the true price, 88.842, sits a little above the duration-only estimate of 88.492.

## Sources

- U.S. Treasury, [31 CFR Part 356, Appendix B](https://www.ecfr.gov/current/title-31/subtitle-B/chapter-II/subchapter-A/part-356/appendix-Appendix%20B%20to%20Part%20356), section II: formulas for converting yields to prices, with worked examples.
- Municipal Securities Rulemaking Board, [Rule G-33, Calculations](https://www.msrb.org/Rules-and-Interpretations/MSRB-Rules/General/Rule-G-33): price from yield with compound discounting, and simple interest when one coupon period or less remains.
- Frederick R. Macaulay, *Some Theoretical Problems Suggested by the Movements of Interest Rates, Bond Yields and Stock Prices in the United States since 1856* (NBER, 1938), chapter [The Concept of Long Term Interest Rates](https://www.nber.org/system/files/chapters/c6342/c6342.pdf): the origin of duration.
- Microsoft Support, [MDURATION function](https://support.microsoft.com/en-us/office/mduration-function-b3786a69-4f20-469a-94ad-33e5b90a763c) and [PRICE function](https://support.microsoft.com/en-us/office/price-function-3ea9deac-8dfa-436f-a7c8-17ea02c21b0a): their worked examples (5.736 and 94.63) are among the cases this calculator is tested against.

## Questions

**Why does the price fall when the yield rises?**

The coupons and face value are fixed, so a higher discount rate makes each one worth less today. A buyer will only accept the old coupon at a higher yield by paying less for the bond.

**Is duration the same as the time to maturity?**

No. Coupons arrive before maturity, so the weighted average time is shorter. Only a zero-coupon bond has a Macaulay duration equal to its time to maturity.

**Why is the accrued interest zero?**

With a whole number of coupon periods, such as 10 years paid semiannually, the bond settles on a coupon date and nothing has accrued. Enter dates, or a term such as 7.3 years, to see accrued interest and the gap between clean and dirty price.