The most difficult aspect of collecting and redeeming frequent flier miles is trying to determine how much those miles are worth. Without that information, you won't know if you should use miles in one program or another, or simply pay cash. Knowing how much your miles are worth also provides useful context for earning them. A program that requires more miles for award tickets may be the best option if it also awards more miles in the first place.But exact valuation is highly subjective. Except for a few loyalty programs that specify the cash value of their miles (e.g., Southwest Airlines says each Rapid Rewards point is worth about 1.4 cents for discounted Wanna Get Away fares), determining how much your miles are worth depends on your own travel needs. One of the most popular strategies is to find a balance between the cost of those miles and the value you assign to the award you book with them (which is not necessarily the cost of a regular ticket.)See: Best Airline Rewards Programs of 2014-15Opportunity cost is the price you pay when you could have done something else. For example, if Tom earns 25,000 miles in the course of his travels, then he didn't really pay for those earned miles — they were a free benefit associated with a frequent flier program. But if he purposely flew on a particular airline to earn those miles, then he probably sacrificed booking a cheaper fare. The extra money he paid for flying on a preferred carrier is the cost of earning those miles. If he paid $125 extra overall, those 25,000 miles are worth at least a half-cent each.Meanwhile, Alice also earned 25,000 miles, but she did it without flying. She spent $25,000 on an airline-affiliated credit card that awards her 1 mile per dollar. If her alternative was to use a cash-back card that earns 1 percent, then the opportunity cost of her miles was the $250 in cash-back that she failed to collect. This means Alice's miles are worth at least a penny each.Both Tom and Alice have established a floor for the value of their miles, and they learned that even free miles have a cost associated with the choices they made. This cost is fairly easy to calculate if you know what your other options were. But the difficult part of calculating the value of your miles is trying to determine how much they're worth when you redeem them.One of the greatest benefits of using miles is that most programs require the same number of miles between any two points in the same zone, regardless of the actual published fare. For example, a domestic roundtrip ticket within the United States might cost 25,000 miles at the discounted saver level (which has capacity restrictions). That same award price exists whether you want to book a $150 ticket between Seattle and San Francisco or a $600 ticket between Los Angeles and New York.Clearly, Alice should not use the miles for which she paid $250 in order to book a $150 ticket. Tom could book either and still come out ahead, but it would be preferable if he used them for the more expensive flight. This is why you should examine both sides of the transaction: Earning miles cheaply doesn't mean you can or should redeem them for every opportunity that comes along.Extracting value from the difference between the price paid and the redemption value is called arbitrage. It's at the heart of "mileage running," a hobby in which people will book cheap tickets to a destination and fly back the same day for the sole purpose of earning miles to pay for a more expensive ticket.See: How to Book Your Next Award Flight Like a ProInternational travel, especially in first and business class, offers one of the best values for mile redemption. In many cases, the number of miles required for a business-class fare is only 50 percent more than for economy class, and first class may cost only 100 percent more than economy class. Cash fares, however, can be between five and 10 times more expensive.The catch is that you probably would never purchase a $10,000 international first-class fare from Los Angeles to Hong Kong. You might not even have the resources or desire to pay the $1,500 it costs to fly in economy class.Miles and points can let you take some amazing trips, but always consider what you would have paid if some imaginary coupon were available. Maybe $2,000 is the right valuation for a first-class award that costs 100,000 miles, or about 2 cents each.For another perspective, imagine Tom and Alice each have family to visit in New York. This makes a $600 ticket from Los Angeles to New York mandatory whether they choose to pay for it with miles or dollars. No imaginary coupon is necessary — they would have paid $600.Award travel can still offer incredible value when used for regular economy fares. These tickets tend to have very flexible rules, requiring the same number of miles whether you're making connections or traveling nonstop. Customers with elite status in a loyalty program can make changes or cancel a ticket with no fees, compared to nonrefundable cash fares that impose fees on everyone. Even people without elite status may be able to make limited changes to award tickets for free, something they can't do with most nonrefundable fares.The price for cash fares also tends to increase drastically as the departure date draws nearer, with the expectation that last-minute travelers are insensitive to price. Prices for award travel do not change, and award availability can actually improve. That's why it's a good idea to hold some miles in reserve for emergency travel.Evaluating alternative options, your travel needs and your desire for a more comfortable travel experience is critical to understanding the value of your frequent flier miles. It's rare that this can be distilled to a single number that applies to everyone, but doing a little math on your own will give you the confidence that you're obtaining valuable benefits from your hard-earned miles.See: Which Travel Rewards Program Should You Join?About the author: Scott Mackenzie learned how to travel and earn elite status on the cheap during graduate school. He now shares these tricks on the blog Travel Codex. You can also follow him on Twitter @Travel_Codex.