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Modified Duration Calculator

Quick answer

ModDur = Duration ÷ (1 + y/k): a 4.46-year duration at 8% annual yield gives 4.21 — prices fall ≈4.21% per 1% rate rise.

  • Results update as you type.

Figures are estimates from this calculator’s standard formula — adjust the inputs in the tool below for your exact number.

How Does the Modified Duration Calculator Work?

Modified duration = Macaulay duration ÷ (1 + y ÷ k)

Modified duration converts a bond's Macaulay duration into a price-sensitivity number: the approximate percentage price change for a one-point yield move. Mathematically, the engine applies Modified duration = Macaulay duration ÷ (1 + y ÷ k). A 5-year 6% annual-coupon bond at par has a Macaulay duration of ≈4.46 years; at an 8% yield its modified duration is 4.46 ÷ 1.08 ≈ 4.13 — a +1% rate rise drops the price ≈4.13%. Everything you enter stays in your browser, and the answer appears in the same units as your inputs the moment the figures are complete.

  1. 1

    Step 1

    Fill in each input field with your own data.

  2. 2

    Step 2

    The tool runs the formula Modified duration = Macaulay duration ÷ (1 + y ÷ k) on your figures.

  3. 3

    Step 3

    Review the result displayed on screen.

  4. 4

    Step 4

    Refine the inputs until the numbers fit your case.

Use Cases

Rate-risk budgeting

Capping portfolio sensitivity before rate events

Bond comparison

Weighing two candidates' rate exposure

Immunization design

Matching duration to a liability date

Scenario stress tests

Pricing a 1–2% rate shock quickly

Common Mistakes

  • Confusing the two durations

  • Ignoring compounding frequency

  • Extrapolating big moves

FAQs

Duration vs modified duration?

Macaulay duration is a weighted payback time in years; modified divides by (1+y) to become a sensitivity — the practical one for traders.

Why is the estimate approximate?

The price-yield curve is convex: duration is the tangent line, accurate for small moves and increasingly off for big ones — convexity corrects it.

What formula does the Modified Duration Calculator use?

It computes Modified duration = Macaulay duration ÷ (1 + y ÷ k) — with y is the yield to maturity and k the coupons per year.

How do I know the result is right?

The Modified Duration Calculator uses the standard closed-form formula shown above; the accuracy depends only on the figures you supply.

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