Convexity helps to approximate the change in price that is not explained by duration. If you go back to the third property of a bond's price volatility you will see that when there is a large change in rates, the duration measure can be way off because of the convex nature of the yield curve.
To calculate convexity the formula is:
Formula 14.16
Convexity adjustment to the percentage price change = C x change in yield squared x 100 
To find the C in the equation, use this equation that has the same notation as duration:
C = V3 +V2  2(V1) / 2V1(change in yield) squared
Estimate a Bond's Price Given Duration, Convexity and Change in Yield
This is done by simply adding the convexity adjustment and the percentage price change due to duration equations to achieve an estimate that is closer than just a duration measure.
Formula 14.17
Total Price change = (duration x change in yield x 100) + (C x change in yield squared x 100) 
Example: Total Price Change
Using the Stone & Co. bonds that had duration of 5.5, let's add a convexity of 93 and an increase of 150 bps in yield.
Answer: Price Increase
Total Price Change = (5.5 x .0150 x 100) + (93 x .0150 squared x 100)
= 8.25 + 2.0925
= 6.157
So if rates increase by 150 bps, the price will decrease by 6.157%
Now let's look at a decrease of 150 bps in yield.
Answer: Price Decrease
Total Price Change = (5.5 x .0150 x 100) + (93 x .0150 squared x 100)
= 8.25 + 2.0925
= 10.34
So if rates decrease by 150 bps, the price will increase by 10.34 %
Again, if you refer to the properties of price volatility, you can see that as rates decrease, the price increase will be greater than the decrease in price when rates rise.
Modified Convexity vs. Effective Convexity
With modified convexity the cash flows do not change due to a change in interest rates.
Effective Convexity, on the other hand, assumes that cash flow does change due to a change in interest rates.
When bonds have options, it is best to use effective convexity just like you should use effective duration. For optionfree bonds, either convexity measure will be a positive value, whereas when it comes to bonds with options, the effective convexity could be negative even if the modified convexity is positive.

Investing
Explaining Convexity
Convexity is the measure of the curve in the relationship between a bondâ€™s price and its yield. 
Investing
Immunization Inoculates Against Interest Rate Risk
Bigmoney investors can hedge against bond portfolio losses caused by rate fluctuations. 
Investing
Use Duration And Convexity To Measure Bond Risk
Find out how this measure can help fixedincome investors manage their portfolios. 
Investing
Why You Should Avoid Fixating on Bond Duration
Financial advisors and their clients should then focus on a bond fundâ€™s portfolio rather than relying on any single metric like duration. 
Investing
Advanced Bond Concepts
Learn the complex concepts and calculations for trading bonds including bond pricing, yield, term structure of interest rates and duration. 
Investing
Treasuries Rout May Deepen on Mortgage Hedging
Fed rate hikes may spur mortage bond owners to sell Treasuries to reduce their exposure to rising rates 
Financial Advisor
Why Bondholders Should Manage Duration Risk
Bonds and bond funds are fixedincome investments, but their duration, combined with changes to interest rates, can lead to price fluctuations.