# Bond Price, Duration and DV01 Calculator

> Free bond calculator. Enter face value, coupon, yield to maturity, years and payment frequency to get the bond price, current yield, duration and DV01.

Source: https://learn.tradelabsai.com/tools/bond-calculator/  
Track: Calculators · Level: Beginner · Updated: 2026-10-03  
Publisher: TradeLabs AI (https://tradelabsai.com). Education, not financial advice.  
Cite as: TradeLabs Learn, "Bond Price, Duration and DV01 Calculator", https://learn.tradelabsai.com/tools/bond-calculator/

A bond's price and its yield move in opposite directions, and how much the price moves for a change in yield depends on the bond's coupon and maturity. This calculator prices a plain fixed coupon bond from its yield to maturity, then measures its interest rate sensitivity with Macaulay duration, modified duration and DV01, the dollar change in price for a one basis point change in yield. It assumes the bond is valued on a coupon date, so there is no accrued interest.

## Calculator

*Interactive calculator: use it at https://learn.tradelabsai.com/tools/bond-calculator/*

## How it works

```
Price = Σ (Coupon / (1 + y)^t) + Face / (1 + y)^n
Macaulay duration = Σ (t × PV of cash flow t) / Price, in years
Modified duration = Macaulay duration / (1 + y)
DV01 = Modified duration × Price × 0.0001
```

Here y is the yield per period (annual yield divided by coupons per year), t counts periods and n is the total number of periods. See [Yield to Maturity](https://learn.tradelabsai.com/bonds-credit/yield-to-maturity/) and [Duration](https://learn.tradelabsai.com/bonds-credit/duration/).

**Example: A 10 year 5% bond at a 4% yield**
A $1,000 bond pays a 5% coupon semi annually, $25 every six months, for 10 years. Discounting at 2% per half year, its price is about $1,081.76, a premium because the coupon is above the market yield. Macaulay duration is about 8.08 years and modified duration about 7.92. DV01 is about $0.86: if yields rise one basis point to 4.01%, the price falls by roughly 86 cents. A 1 percentage point rise in yields would cut the price by roughly 7.9%, about $86, before convexity effects. See [DV01](https://learn.tradelabsai.com/bonds-credit/dv01/) and [Convexity](https://learn.tradelabsai.com/bonds-credit/convexity/).

## Premium, par and discount

| Coupon versus yield | Price | Example |
|---|---|---|
| Coupon above yield | Above par (premium) | 5% coupon, 4% yield |
| Coupon equals yield | At par | 5% coupon, 5% yield gives $1,000 |
| Coupon below yield | Below par (discount) | 3% coupon, 5% yield |

Try changing the yield to 5% in the calculator to see the price move to par.

## What drives duration

| Factor | Effect on duration |
|---|---|
| Longer maturity | Higher duration, more rate sensitivity |
| Higher coupon | Lower duration, since more value arrives early |
| Higher yield | Slightly lower duration |
| Zero coupon bond | Duration equals maturity |

## Using DV01 in practice

Traders use DV01 to size and hedge rate positions. A portfolio of bonds with a total DV01 of $5,000 gains or loses about $5,000 for each basis point move in yields. To hedge, sell futures or swaps with an offsetting DV01. See [Bond Trading](https://learn.tradelabsai.com/markets/bond-trading/) and [Yield Curve Trades: Steepeners, Flatteners and Butterflies](https://learn.tradelabsai.com/bonds-credit/yield-curve-trades/).

## Limitations

1. **No accrued interest:** between coupon dates, quoted (clean) prices exclude accrued interest.
2. **Plain bonds only:** callable bonds, floating rate notes and inflation linked bonds need other models.
3. **Flat yield:** all cash flows are discounted at one yield rather than a full yield curve. See [Yield Curves](https://learn.tradelabsai.com/bonds-credit/yield-curves/).
4. **Linear approximation:** duration understates gains and overstates losses for large moves; convexity corrects this.
5. **Credit risk:** the yield already includes it; the calculator does not model default. See [Credit Spreads](https://learn.tradelabsai.com/bonds-credit/credit-spreads/).

## Trying scenarios

Change one input at a time to build intuition. Raise the yield from 4% to 6% and watch the price fall below par. Shorten the maturity from 10 years to 2 and watch duration and DV01 shrink. Cut the coupon to zero and see duration equal maturity. These experiments show why long dated, low coupon bonds are the most sensitive to interest rate changes.

## Frequently asked questions

### Why do bond prices fall when yields rise?

Because a bond's fixed cash flows are worth less when discounted at a higher rate, so its price must fall to offer the new market yield.

### What is DV01?

The dollar value of a one basis point change in yield: how much the bond's price changes when its yield moves by 0.01 percentage points.

### What does modified duration mean?

The approximate percentage change in a bond's price for a one percentage point change in yield.

Next, chart option outcomes with the [Option Payoff Calculator](https://learn.tradelabsai.com/tools/option-payoff-calculator/).

## Continue learning

- Next lesson: [Option Payoff Calculator](https://learn.tradelabsai.com/tools/option-payoff-calculator/)
- Previous lesson: [Portfolio Volatility and VaR Calculator](https://learn.tradelabsai.com/tools/var-calculator/)
- Related: [Portfolio Volatility and VaR Calculator](https://learn.tradelabsai.com/tools/var-calculator/): Free value at risk calculator. Enter portfolio value, daily volatility, confidence level and horizon to estimate VaR and expected shortfall in dollars.
- Related: [How Bonds Work](https://learn.tradelabsai.com/bonds-credit/how-bonds-work/): A bond is a loan that pays interest and returns principal at maturity. Learn coupons, price and yield, why prices fall when rates rise and the main bond risks.
- Related: [Yield to Maturity](https://learn.tradelabsai.com/bonds-credit/yield-to-maturity/): Yield to maturity is the total return of a bond held to maturity. Learn how YTM is calculated, current yield, yield to call and worst, and YTM's assumptions.
- Related: [Duration](https://learn.tradelabsai.com/bonds-credit/duration/): Duration measures how sensitive a bond's price is to interest rate changes. Learn Macaulay, modified and effective duration, how to calculate them and their uses.
- Related: [DV01](https://learn.tradelabsai.com/bonds-credit/dv01/): DV01 measures how many dollars a bond or portfolio gains or loses for a one basis point change in yield. Learn the formula, hedge ratios and how traders use it.
- Related: [Convexity](https://learn.tradelabsai.com/bonds-credit/convexity/): Convexity measures how a bond's duration changes as yields move, refining price estimates for big moves. Learn the formula, positive and negative convexity and uses.