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The 5 Best Automotive Math Formulas With Jeff Smith

By Jeff Smith February 07, 2020Wait – wait – wait! Don’t just skip this story because the word “Math” appears in the title. You may regret not learning some cool ways to use simple middle-school arithmetic and, okay, some high school geometry to learn something new. Trust us, it will be easy stuff.

Our formulas are easy. Sure, there are dozens of automotive equations that are useful, but they’re also complex and difficult to execute. The most obvious example is the formula for compression ratio. We’re old enough to remember sharpening our pencils, finding an eraser and large legal pad, and spending an hour or two crunching out multiple variations on piston dome, chamber volume, deck height, and head gasket combinations to find an ideal compression ratio. Thankfully, in the 21st Century, there’s no reason to waste time doing that. Several free online compression-ratio programs will crunch the numbers for you.

The long-hand version of the compression ratio equation is cumbersome. That’s why it’s not in our Top 5, but it doesn’t mean you shouldn’t know how it works. Having tossed out that caveat, we’ll make it easy for you. Performance Trends offers access to a convenient compression ratio calculator that you can download for free. Just click on the Performancetrends.com website, find the “downloads” button, and look for the compression ratio calculator.

Short of that, we’d like to think these short-but-sweet equations are worth saving for future reference. We use at least one of these almost every day for technical articles. Some gearheads recoil at the thought of even simple math, but this stuff is elementary and we promise no Ibuprofen will be required to run these numbers.

1. How to Calculate Engine Displacement

How big is it? That’s the classic car guy question, and we can show you how to quickly calculate this based on three simple inputs: bore, stroke, and the number of cylinders. This can be useful, for example, when considering adding a stroker crank.

Way back in high-school geometry class (assuming you were paying attention and not ogling the cute girl in the second row), the volume of a cylinder is calculated using the formula of an area of a circle (bore) times the length of the cylinder (stroke). As our example, we’ll use the ubiquitous 350ci small-block Chevy that is fitted with a 4.00-inch bore and a 3.48-inch stroke (displacement = bore radius x bore radius x π x stroke).

To do this, you must first calculate the area of the bore by finding the radius of the bore. Half of the diameter is the radius, so in this case, it is 2 inches. Next, multiply that by itself (2 x 2), then multiply that times π (3.14159).

Area = Radius x Radius x π (or Radius Squared x π)

2 x 2 x 3.1416 = 12.5664

Now, you are ready to calculate the displacement:

Displacement = Area x Stroke

For our example 350 Chevy engine:

12.5664 x 3.48 = 43.73 cubic inches

All that’s left to do is multiply that volume times the number of cylinders.

43.73 x 8 cylinders = 349.84 cubic inches

There is also a handy shortcut:

Displacement = Bore x Bore x Stroke x 0.7854 x Number of Cylinders

4 x 4 x 3.48 x 0.7854 = 349.8 (rounded to 350)

There’s also an easy way to remember 0.7854 (a simplified constant to convert the bore squared into Pi-R squared.) If you study the four numbers in the upper left-hand quadrant of any hand calculator, you will see these numbers in clockwise sequence. Once you’ve used it a few times, it becomes second nature, and calculating displacement just got really simple.


We recently built this big-block Chevy street engine using a 4.500-inch bore and a 4.250-inch stroke. How big is it? If you got 540ci – you win a gold star.

If you look at the keypad on our well-used calculator, note the numbers in the upper left quadrant. Start with a decimal point then plugin 7-8-5-4. You’ll note this in a square clockwise pattern. You can use this as a way to help you remember the shortcut.