Bond Duration Calculator

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This calculator shows how sensitive a bond’s price is to changes in interest rates.
It helps estimate how much a bond’s value may change when interest rates move.
More info →

Input

Face Value

Coupon Rate (%)

Years To Maturity Decimals are accepted for whole coupon periods, e.g. 5.5 years with semi-annual coupons.

Bond Price (Market Price)

Coupon Frequency

Yield Shift To Test (bps) Used for the price sensitivity below. 100 bps = 1.00%.

Enter bond details to calculate yield to maturity and duration.

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How This Calculator Works

When interest rates rise, bond prices fall. Duration tells you by how much. The calculator first finds the bond's yield to maturity from its price, then works out how long, on average, you wait for its cash flows and how sensitive its price is to a change in yield. It finishes by testing a yield change you choose.

The Formulas

Macaulay Duration = ∑(t × PV_t) ÷ ∑PV_t ÷ f
Modified Duration = Macaulay ÷ (1 + y)
Est. Price Change = (−Modified × Δy + ½ × Convexity × Δy²) × Price

PV_t = cash flow in period t ÷ (1 + y)^t · y = yield per period · f = coupons per year · YTM = y × f · DV01 = Modified × Price × 0.0001

What Each Input Does

Face Value: The amount repaid at maturity.
Coupon Rate (%): The yearly interest paid on the face value.
Years To Maturity: Time until repayment. It must be a whole number of coupon periods (whole years for annual, steps of 0.5 for semi-annual).
Bond Price (Market Price): What the bond costs today. It is used to find the yield to maturity.
Coupon Frequency: Annual or semi-annual coupon payments.
Yield Shift To Test (bps): A yield change to test, in basis points (100 bps = 1%). The default is 100.

Step by Step

The coupon per period and the number of periods are worked out.
The yield that makes the bond's cash flows worth exactly its price is found (like Excel's RATE).
Each cash flow is discounted at that yield, giving the schedule and the durations and convexity.
The price change for your yield shift is estimated with duration and convexity, and compared with the exact re-priced value.

Reading the Result

Modified duration – roughly the % fall in price for a 1% rise in yield.

Higher duration – more interest-rate risk.

Quick Example

Face value 1,000, coupon 8%, 10 years, price 950, annual coupons, shift 100 bps. YTM is 8.77%, Macaulay duration 7.17 years, modified duration 6.59. A 1% rise in yield is estimated to cut the price by about 59.82 to 890.18; re-pricing exactly gives 890.09.