# Calculating the (Surprisingly Positive) Effects of Swapping Carbs for Fats in Your Diet

For decades we have been told by various sources–doctors, fitness experts, and parents, to name a few–that eating fat is bad for you. But there is a growing body of recent research evidence that indicates this blanket statement is not true.

One strand of the research seeks to investigate the different effects on our health that eating different fats have. Three types of fats have received the most attention: saturated fat, monounsaturated fat, and polyunsaturated fat. Various studies have been conducted to examine how these affect health, and heart health in particular. Section 2.1.4 in The Calculus of Happiness discusses one such study (referenced below in the Limitations portion of this webpage), a meta-analysis (a “study of studies”) of 60 controlled trials published between 1970 and 1998. Participants in these studies had their food intake thoroughly controlled, with varying proportions of calories coming from carbohydrates and fats. The meta-analysis’ researchers conducted a statistical analysis of the data and found something remarkable: a relationship between the total-to-HDL ratio (the ratio of the participants’ total cholesterol number to their HDL (“good cholesterol”) number) and the percentage of carbohydrate calories in their diet swapped for saturated, monounsaturated, or polyunsaturated fat calories. Abbreviating total-to-HDL by THR, the percentage of carb calories swapped for saturated fat by s, for monounsaturated fat by m, and for polyunsaturated fat by p, the researchers found that:

$\text{THR}=0.003s-0.026m-0.032p+b,$

where b was the intrinsic THR number (i.e., assuming no swapping of carb calories for fat calories occurred). This equation predicts that swapping carb calories for an equal amount of fat calories raises THR, while swapping them for an equal amount of unsaturated fat (of either kind) lowers THR. The authors cite studies showing that THR is a better indicator of heart disease risk than total cholesterol or individual cholesterol (e.g., LDL) levels. And since lower THR implies a lower risk for heart disease (see this study for a discussion of how much the risk drops by), the formula above contains valuable insight into how the macronutrient composition of a diet affects the risk of developing cardiovascular disease while following that diet.

The calculator below helps you estimate the THR ratio that would result assuming you swapped carb calories for the different fats appearing in the THR formula. Feel free to insert your own values into the green cells to get the new THR estimate. (If you don’t know your current THR, leave that value as 5, and by changing the rest of the values in the green cells you’ll get an estimate of how your THR might change as you swap carb calories for different fat calories.)

## Limitations

The study mentioned is: Mensink, R. P., et al., “Effects of Dietary Fatty Acids and Carbs on Blood Lipids,” American Journal of Clinical Nutrition, 77 (2003), pgs. 1146–1155. The authors cite several limitations of their study, including the fact that “the studies included in our meta-analysis lasted between 13 and 91 d [days].” As they state, “this raises the question of whether the effects observed are transitory.” See also the discussion in Section 2.1.4 of The Calculus of Happiness regarding the error ranges of the coefficients in the THR formula. In particular, while the error ranges for the coefficients for and still keep those coefficients negative, the error range for the coefficient includes both positive and negative numbers. This means the authors can’t be sure if swapping carb calories for saturated fat calories raise or lowers THR.