Gamma confuses some options traders because it's a "secondary" indicator. It measures the speed of change in another indicator, delta.
Delta measures the rate of premium change in the options related to changes in the underlying (and of course is affected by time and proximity). Gamma measures how quickly delta moves. It tracks delta and reflects changing volatility, so looking at delta and gamma together is a great way to compare volatility between two or more issues.
Delta is measured with a single "outcome" value. So delta of 1.0 tells you that the option is moving exactly the same degree as the underlying. If delta is 0.75 it means the option changes 75 cents for every point of movement in the underlying. In comparison, gamma tells you how responsive delta is, meaning how quickly it changes. This quantifies the tendency in the options market for options pricing to lag behind stock price movement. The faster the reaction of option premium to the underlying movement, the higher its volatility -- that is gamma in a nutshell. Knowing the approximate gamma level helps you to judge market risk, by placing a simple value on volatility. You see this based on proximity and time. The closer to ATM an option becomes, the more likely you are to see gamma increase; and as the option moves farther ITM or OTM, the lower gamma is likely to be.
Options traders are always wishing for the perfect "cause and effect" in premium changes versus underlying price movement. But this is not a reliable ideal, and it is rarely achieved. Options pricing is unpredictable (as if you didn't know that already), but the point is that unpredictability is why you need both delta and gamma. With gamma, you are better equipped to view delta changes in view of proximity of strike to underlying price, and to watch it evolve as expiration approaches. This is a reliable way to estimate the volatility factor in overall value, and of seeing how IV works with different underlying securities.
Rather than trying to calculate delta or gamma, why not rely on a free online calculator? The CBOE provides a free calculator that provides you with all of the Greeks. Go to CBOE Options Calculator where you can track gamma, delta and other indicators.