What is Macaulay duration?

Macaulay duration is the present-value-weighted average time (in periods) until a bond's cash flows are received. A zero-coupon bond's Macaulay duration equals its maturity; coupon bonds are shorter because interim coupon payments arrive earlier.

How does Macaulay duration differ from modified duration?

Modified duration = Macaulay duration / (1 + periodic YTM). Modified duration estimates the percentage price change for a 1% change in yield, while Macaulay duration is a time-weighted measure of cash-flow timing.

What inputs do I need?

Face value, annual coupon rate (%), yield to maturity (%), coupon frequency (annual or semi-annual), and total number of coupon periods to maturity.

Why does a higher coupon rate lower duration?

Higher coupons front-load cash flows, so more of the bond's value is received in early periods. That pulls the PV-weighted average time closer to the present, reducing Macaulay duration.

Can I use this for semi-annual coupon bonds?

Yes. Select "Semi-annual" and enter total semi-annual periods. The calculator uses the periodic yield (annual YTM / 2) and reports duration in semi-annual periods. Divide by 2 to convert to years.

Macaulay Duration Calculator

Name: Macaulay Duration Calculator
Availability: InStock
Author: Nham Vu

Enter face value, coupon rate, YTM, and periods to get Macaulay duration, modified duration, and a full cash-flow weight breakdown.

Bond Parameters

Face Value ($)

Annual Coupon Rate (%)

Annual YTM (%)

Coupon Frequency

Total Periods to Maturity

= 3 years (semi-annual)

Macaulay Duration

—

periods

Modified Duration

—

% per 1% yield

Bond Price

—

per $1,000 face

DV01

—

$ per bp

Cash-Flow Breakdown

How each period contributes to Macaulay duration

Period	Cash Flow	PV	Weight	t × Weight

Enter bond parameters and click Calculate

Summary

Enter face value, coupon rate, YTM, and periods to get Macaulay duration, modified duration, and a full cash-flow weight breakdown.

How it works

Enter the bond's face value, annual coupon rate, and yield to maturity (YTM).
Choose the coupon frequency (annual or semi-annual) and the total number of coupon periods.
Each period's cash flow is discounted to present value using the periodic yield.
Each PV is multiplied by its period number, then summed and divided by the bond price to get Macaulay duration.
Modified duration is Macaulay duration divided by (1 + periodic YTM).
The cash-flow table shows each period's payment, PV, weight, and contribution to duration.

Use cases

Measuring interest rate risk of a bond before adding it to a portfolio.
Immunizing a fixed-income portfolio by matching Macaulay duration to an investment horizon.
Comparing two bonds with the same maturity but different coupons to find the lower-risk one.
Teaching bond pricing concepts by visualizing how each cash flow contributes to duration.
Computing the starting point for modified duration and DV01 estimates.

Frequently Asked Questions

Last updated: 2026-07-23 · Reviewed by Nham Vu