Hı, I am beginner in cycling . I learned my body's Base Metabolic Rate (BMR) is burning 1700 calories at rest.
For example I burned 2000 calories in 4 hour cycling workout. Should I eat 2000 burnt calories + 1700 bmr calories = 3700 calories after bicycle ride?
All the numbers above are estimates. You should interpret things more like: given your weight, height, and sex, your basal metabolic rate (BMR) is 1,700 +/- a couple hundred calories. The estimate you got for your energy expenditure during cycling is in addition to your BMR.
However, there is also a range of plausible values around that estimate. The OP mentioned in comments that it's based on heart rate, so the estimate has more uncertainty than power meter estimates (which still have a range of uncertainty!), and the HR estimate is possibly biased high.
Don't treat your estimated total calorie expenditure as an exact number, and don't base your consumption exactly on it - you also don't know the exact calories in your food, especially if you cooked from scratch.
I don't have a biology or related background. I am confident that all the biological statements below are close to correct, even if a specialist would probably quibble. I have provided sources. Any statements about math/statistical issues have higher confidence (I have a PhD in an applied statistical field).
First, the OP probably used a model to tell them their estimated basal metabolic rate - or more specifically, the average resting energy expenditure given some characteristics (age, sex, and weight are common ones). The Harris-Benedict equation is one such model.
Scientists use indirect calorimetry to directly measure your energy expenditure. They basically seal you in a room and measure your carbon dioxide production (our bodies generate energy by oxidizing adenosine triphosphate to adenosine diphosphate, producing CO2 in the process). From there, they can use linear regression (or related techniques) to estimate the relationship between observable variables (e.g. age, sex, weight) and calorie expenditure.
Remember that not everyone is average. This applies to the formula for (average!) maximum heart rate, 220 minus age. I have observed heart rates about 10 beats/min higher than my model predicted rate, and yet I survive. Conversely, some people will have lower max HR than their prediction. Basically, you should assume that your own BMR may be something like a couple hundred calories on either side of the average BMR predicted from the model. For example, most of the human population with your characteristics should be within 1500-1900 calories BMR, and yours probably is - although you won't know for certain without doing a study in a metabolic chamber.
Second, calories burned during exercise are also estimates. For issues from translating power meter numbers to actual calories, this answer has some more detail. But basically, power meters directly measure the work done to the bicycle, but your body is not 100% efficient and it has to burn more energy to do that work; we have estimates of human gross mechanical efficiency, but there are similar estimation issues as in the paragraph above. The answer I linked has a worked example. The same would hold true for heart rate monitors and their derived energy expenditures, only these are also thought to be less accurate than something like a power meter and also biased high.
Thus, treat calorie management as an approximate process, and rely on your sense of satiety. Remember that you also don't know the exact calories in your food - you can estimate the likely caloric content based on estimates others have published or on nutrition labels, but even with processed food there may be some variability from batch to batch due to manufacturing variances, or perhaps the manufacturer managed to get their published counts to skew a bit lower than actual.
Power meters can be very useful tools for training and pacing. It does not seem cost-effective to me to get a power meter just to get more accurate calorie counts, especially given the issues outlined above. However, structured training can be more efficient at improving your fitness, and it can help you break out of a plateau relative to just unstructured rides. Serious cyclists should consider one - although one can train successfully without a power meter as well.
As a side note not related to the question, some athletes need to pay attention to under-fueling as well. Persistent under-fueling can create relative energy deficiency in sports (RED-S), a syndrome that impairs sports performance, bone density, reproductive health, and various other health parameters. It can affect both women and men. This is not a reflection on the OP. However, in weight-sensitive sports, some of us probably can err on the side of over-controlling our intake, and thus under-fueling. This can be influenced by cultural factors as well (e.g. wider pressure on women to be thin, sports-specific encouragement to be light). I'd urge readers to be aware of this, and to seek help if you feel like this might apply to you.
Assuming the estimates are accurate you’ll have burned 3700kcal on that day and have to replenish them with food.
As Weiwen already hints, don’t just eat after a ride, eat before and during the ride as well to keep your carb levels up and avoid “hitting the wall”. Easily digestible carbohydrates are your best friend for long exercise sessions.
