# Bond Convexity Calculator

URL: https://speedycalculator.com/calculators/finance/bond-convexity/
Last updated: 2026-10-25

> The bond convexity calculator works out a bond's price, coupons and convexity – how the price–yield relationship curves – using the price change for a yield shift up and down.

## 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
- Bond convexity
- Effective duration

## Formula

```
Price P = Σ coupon ÷ (1 + y/f)^t + face ÷ (1 + y/f)^N
Convexity ≈ (P₋ + P₊ − 2P) ÷ (P × Δy²)
Price change ≈ −duration × Δy + ½ × convexity × Δy²
```

## Explanation

Duration gives a straight-line estimate of how a bond's price changes with yields; convexity corrects for the curve. Higher convexity is valuable: prices rise more when yields fall than they drop when yields rise.

### How to use the Bond Convexity 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 face value, coupon rate, frequency, years to maturity, yield to maturity and the yield shift to use.

### 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)
- **Bond convexity** = ([Price if yield falls] + [Price if yield rises] - 2×[Bond price])÷([Bond price]×([Yield differential (shift)]÷100)^2)
- **Effective duration** = ([Price if yield falls] - [Price if yield rises])÷(2×[Bond price]×[Yield differential (shift)]÷100)

### Example values

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

Face valueBond convexity50071.85275071.8521,00071.8521,25071.8521,50071.8522,00071.852

## 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; **Bond convexity = 71.852**; Effective duration = 7.677.

## FAQ

**What is bond convexity?**
A measure of how the duration of a bond changes as yields change.

**Is higher convexity good?**
Yes, for the holder – prices gain more on falls in yield than they lose on rises.

**Which bonds have more convexity?**
Long-term, low-coupon bonds.

**What formula does the Bond Convexity Calculator use?**
Price P = Σ coupon ÷ (1 + y/f)^t + face ÷ (1 + y/f)^N.


## Sources

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