The short answer
Per diem equals the daily rate times the trip days, and the daily rate equals the lodging rate plus the meals and incidentals rate. Write it as one formula: per diem = (lodging rate + meals rate) × trip days. With $98.00 lodging, $59.00 meals and 5 days, the daily rate is $157.00, and $157.00 times 5 is $785.00. Keep the two parts separate all the way through, because expense policies almost always cap lodging and meals separately, and a single combined total hides which side is over its limit.
Step 1: Find the lodging rate and the meals rate
Start with the two rates that apply to the trip. The lodging rate is the nightly allowance for the hotel, and the meals rate covers food plus small incidental costs such as tips and local transport. These rates come from the employer's travel policy or, for government travel, from the agency rate table for the destination city and year. Rates vary by place: a large city pays more than a small town, and rates are revised from time to time, so use the table that applies to the trip dates, not a rate remembered from a previous trip. In this guide the rates are $98.00 for lodging and $59.00 for meals, chosen as round example figures. If the policy gives a single combined daily rate instead of two parts, split it before you go further, because the checking step at the end needs the parts.
Step 2: Add the two rates to get the daily rate
Add lodging and meals to get what one day of the trip is worth. Here that is $98.00 plus $59.00, which is $157.00 a day. This daily rate is the number to sanity-check first: if it looks far too high or far too low for the destination, one of the two rates is probably wrong, or a partial-day rule is being missed. A daily rate also makes comparisons easy. A five-day trip at $157.00 a day and a seven-day trip at the same rate differ by exactly two days of allowance, which is $314.00, and that kind of quick comparison is how most travel budgets are first sketched.
Step 3: Multiply the daily rate by the trip days
Multiply the daily rate by the number of days the trip runs. Here that is $157.00 times 5 days, which is $785.00. For the expense report, also work out the two parts separately: lodging is $98.00 times 5, which is $490.00, and meals are $59.00 times 5, which is $295.00, and $490.00 plus $295.00 is $785.00, which cross-checks the total. Counting days is where most errors happen. A trip from Monday morning to Friday evening is 5 days, but a trip that starts Sunday night and ends Friday is 6 days, and an overnight trip that returns the next morning is 2 days, not 1, because the traveller sleeps away from home on one night and travels on two calendar days.
Step 4: Check the split, then adjust for partial days
Compare each part against its own limit before you call the total done. If the hotel actually cost $120.00 a night, the lodging side is $600.00 for 5 days against a $490.00 allowance, which is $110.00 over, even though cheap meals might bring the combined total back under $785.00. A combined total cannot fix an over-limit part, because the caps apply separately. Then adjust for the rules this simple version leaves out. Many policies pay a reduced meals rate, often 75%, on the first and last travel days, and many deduct a provided meal from the day's meals rate. Apply those adjustments to the meals side only, and re-add the parts to get the final allowance.
Working backwards
The same formula runs backwards. To find the days for a target allowance, divide the target by the daily rate: $942.00 divided by $157.00 is exactly 6 days, so a 6-day trip at these rates pays $942.00, while 5 days pay $785.00 and 7 days pay $1,099.00. To find the lodging rate for a target, divide the target by the days and subtract the meals rate: $850.00 over 5 days is $170.00 a day, minus $59.00 meals, which is $111.00 a night for lodging. And to stay under a cap, divide the cap by the daily rate and round down: $1,000.00 divided by $157.00 is 6.36, so 6 days at $942.00 is the most that stays under $1,000.00, while 7 days at $1,099.00 overshoot.
Common mistakes
The most common mistake is treating per diem as a reimbursement. It is not. A per diem is a flat allowance, so spending $70.00 on a hotel when the lodging rate is $98.00 does not reduce the allowance, and spending $130.00 does not raise it. The second mistake is measuring the trip in nights instead of days, which drops a travel day and understates the allowance by a full daily rate. The third mistake is adding the two rates wrongly by averaging them, or multiplying only one part by the days and adding the other part once. Both parts are daily rates, so both get multiplied by the days. The fourth mistake is using last year's rates or another city's rates, which makes the whole calculation neat, correct and wrong.
Frequently asked questions
How do you calculate per diem?
Add the lodging rate and the meals rate, then multiply by the trip days. ($98.00 + $59.00) × 5 is $785.00.
What is the lodging part of the example?
$490.00. $98.00 a night times 5 days, against $295.00 for meals.
How many days give $942.00 of per diem?
6 days at $98.00 lodging and $59.00 meals. 5 days give $785.00 and 7 days give $1,099.00.
Do first and last days pay the full rate?
Not always. Many policies pay a reduced meals rate on travel days, so check the policy and adjust the meals side before filing.
Try it on your own trip: put your lodging rate, meals rate and days into the per-diem-calculator, and check the lodging and meals totals separately against your policy caps.