# Effective Duration Calculator

URL: https://speedycalculator.com/calculators/finance/effective-duration/
Last updated: 2026-10-25

> The effective duration calculator measures a bond's price sensitivity to interest rate changes by re-pricing it for a yield shift up and down, and estimates the price change for any rate move.

## Inputs

- Face value
- Annual coupon rate (%)
- Coupon frequency
- Years to maturity
- Yield to maturity (YTM) (%)
- Yield differential (shift) (%)

## Results

- Coupon per period
- Annual coupon
- Bond price
- Price if yields fall by the shift
- Price if yields rise by the shift
- Effective duration
- Approximate price change for a 1% rise

## Formula

```
Effective duration = (P₋ − P₊) ÷ (2 × P₀ × Δy)
Price change ≈ −duration × Δy × price
```

## Explanation

A duration of 7 means the bond's price falls about 7% if yields rise by one percentage point. Effective duration is the right measure for bonds whose cash flows can change, such as callable bonds and mortgage-backed securities.

### How to use the Effective Duration Calculator

- **Face value**
- **Annual coupon rate**
- **Coupon frequency**
- **Years to maturity**
- **Yield to maturity (YTM)**
- **Yield differential (shift)**

Results update as you type, and every field accepts the units shown in its menu.

### How it works

Enter the bond details, the yield to maturity and the yield shift.

### Tips

- Check whether rates are quoted annually, semi-annually or per period.
- Bond prices and yields move in opposite directions – a higher yield means a lower price.
- Use the bond's clean price (without accrued interest) for yield calculations.
- Credit ratios are most useful when tracked over several years.

### Common mistakes to avoid

- Confusing the coupon rate with the yield.
- Using the face value instead of the market price.
- Forgetting that callable bonds may be redeemed before maturity.

### Inputs explained

FieldWhat to enterFace valueAmount in your currencyAnnual coupon rateIn %Coupon frequencyChoose one: Annually, Semi-annually, Quarterly, MonthlyYears to maturityA numberYield to maturity (YTM)In %Yield differential (shift)In %

### What each result means

- **Coupon per period** = [Face value]×[Annual coupon rate]÷100÷[Coupon frequency]
- **Annual coupon** = [Face value]×[Annual coupon rate]÷100
- **Bond price** = bondpx([Face value], [Annual coupon rate]÷100, [Coupon frequency], [Years to maturity], [Yield to maturity (YTM)]÷100)
- **Price if yields fall by the shift** = bondpx([Face value], [Annual coupon rate]÷100, [Coupon frequency], [Years to maturity], ([Yield to maturity (YTM)] - [Yield differential (shift)])÷100)
- **Price if yields rise by the shift** = bondpx([Face value], [Annual coupon rate]÷100, [Coupon frequency], [Years to maturity], ([Yield to maturity (YTM)] + [Yield differential (shift)])÷100)
- **Effective duration** = ([Price if yields fall by the shift] - [Price if yields rise by the shift])÷(2×[Bond price]×[Yield differential (shift)]÷100)
- **Approximate price change for a 1% rise** = -[Effective duration]

### Example values

How the main result changes when **Face value** changes and everything else stays at the example values above:

Face valueEffective duration5007.6777507.6771,0007.6771,2507.6771,5007.6772,0007.677

## Worked example

Inputs — Face value: $1,000; Annual coupon rate: 5 %; Coupon frequency: Semi-annually; Years to maturity: 10; Yield to maturity (YTM): 6 %; Yield differential (shift): 1 %.

Results — Coupon per period = $25.00; Annual coupon = $50.00; Bond price = $925.61; Price if yields fall by the shift = $1,000.00; Price if yields rise by the shift = $857.88; **Effective duration = 7.677**; Approximate price change for a 1% rise = -7.68 %.

## FAQ

**What is effective duration?**
A measure of price sensitivity to yield changes, based on re-pricing.

**How is it different from modified duration?**
It works for bonds with embedded options whose cash flows change with rates.

**What does a duration of 5 mean?**
About a 5% price change for a 1 percentage point change in yields.

**What formula does the Effective Duration Calculator use?**
Effective duration = (P₋ − P₊) ÷ (2 × P₀ × Δy).


## Sources

- [Corporate Finance Institute – financial ratios](https://corporatefinanceinstitute.com/)