Finance & Money
Bond Duration Calculator
Apply an annual-coupon closed-form approximation, convert to modified duration, and estimate price movement for the entered yield shock without hiding convexity limitations.
Annual coupon cash-
Coupon rate as decimal-
Yield as decimal-
Approximate Macaulay duration-
Approximate modified duration-
Duration-only price change-
Estimated price after yield change-
Decision view
Bond yield shock and duration sensitivity
Bond yield shock and duration sensitivityThe first-order price estimate is anchored to the entered clean price and modified duration.
Exact scenario comparisonYield-change scenario (percentage points) changes while all other entered assumptions remain constant.
| Yield-change scenario (percentage points) | Annual coupon cash | Coupon rate as decimal | Yield as decimal | Approximate Macaulay duration | Approximate modified duration | Duration-only price change | Estimated price after yield change |
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How to use Bond Duration Calculator
- Use clean price, coupon, yield, and maturity from the same date.
- Enter the yield change in percentage points.
- Treat the estimate as local sensitivity rather than a forecast.
Calculator guide
Understanding Bond Duration Calculator
Modified duration estimates the first-order price response to a yield change, while Macaulay duration describes the timing-weighted cash-flow horizon.
Calculation method
How the calculation works
Apply a closed-form annual-coupon duration approximation and use modified duration to estimate first-order price sensitivity to a selected yield change. Calculate annual coupon and yield decimals, estimate Macaulay duration, divide by one plus yield for modified duration, and multiply price by negative duration and yield change.
Sensitivity use
Interpret duration as a shock estimate
Duration supports scenario analysis, not a promised market price.
Worked situations
Practical examples
- A positive yield shock usually produces a negative price change.
- Longer duration means greater first-order sensitivity.
- Large shocks make convexity more important.
Better inputs
Useful tips
- Use cash-flow software for trading decisions.
- Check embedded options.
- Compare effective duration for callable bonds.
Before relying on the result
Limitations and common mistakes
- Annual coupons, fixed cash flows, and a parallel local yield change are assumed.
- Convexity, accrued interest, options, default, curve shape, and irregular periods are excluded.
- The closed-form approximation can fail for unusual inputs.
Reference
Key terms
- Macaulay duration
- Present-value-weighted average timing of cash flows.
- Modified duration
- Approximate percentage price sensitivity to yield.
- Yield shock
- Entered change in yield expressed in percentage points.
- Convexity
- Curvature correction omitted from the first-order estimate.
Important note
Calculated from the entered values and stated financial terms. It is not a product quote, lending decision, tax filing, or investment recommendation.
Frequently asked questions
Why is the price change negative for rising yield?
Existing fixed cash flows become less valuable relative to the higher market yield.
Is duration measured in years?
Macaulay duration is; modified duration is commonly interpreted as sensitivity.
Does the estimate include convexity?
No.
Can it value a callable bond?
Not reliably.