RPM Calculator

How the rpm calculator works

Engine speed and road speed are tied together by three things: the gear you are in, the rear end ratio and the size of the tire. Multiply the transmission gear by the rear end gear and you get the overall ratio; divide road speed by the tire's circumference and you get how fast the tire turns. Put the two together and the engine rpm at any speed follows, which is what this rpm calculator works out for every gear at once. Choosing those ratios in the first place is the job of the gear ratio calculator; this page is about what the engine does with them.

The three tabs answer three questions. RPM at speed works as an rpm at speed calculator and a mph to rpm calculator, with torque converter slip for automatics. Top speed is a top speed calculator and a transmission speed calculator in one: the speed every gear reaches at the redline. Shift points is a shift point calculator: the rpm the engine falls to after each upshift, drawn as the familiar sawtooth.

What to enter and where to find it

• Transmission gear ratios. First gear to top gear, from the transmission's specification sheet or service information. Gearboxes that share a case often have different ratios, so check the exact version.
• Rear end gear ratio. From the axle tag, the build paperwork or the tooth counts stamped on the ring gear.
• Tire diameter. The overall diameter of the driven tire; the tire size calculator converts a size code. A loaded tire rolls on a slightly smaller diameter than its nominal size, so real rpm runs a little above the figure here. The maker’s revolutions-per-mile figure is more accurate: to use it, enter 20,168 ÷ revolutions per mile as the tire diameter, in inches.
• Torque converter slip. Zero for a manual or a locked converter. For an unlocked converter, measure it as described in the next section.
• Redline and shift rpm. The redline sets the top of the chart and the top-speed figures; on the Top speed tab any rpm works, such as the rpm of your power peak. The shift rpm is where you upshift.

Torque converter slip

A torque converter couples the engine to the transmission through fluid, so the turbine that drives the transmission always turns a little slower than the engine, until a lockup clutch, if the converter has one, ties the two together. The difference is the slip, a share of engine speed: slip = (engine rpm − transmission input rpm) ÷ engine rpm. The engine therefore has to turn faster than the gearing alone asks for, and engine rpm = rpm from the gearing ÷ (1 − slip).

Slip changes all the time. It is largest when the car pulls away or accelerates hard, smallest on a light, steady cruise, and gone once a lockup converter locks. Rather than guess a figure, measure it: hold a steady speed on a level road, read the tachometer (an engine-rpm reading from a scan tool or data logger is more precise than the dash tachometer), and compare it with the rpm this calculator gives with slip set to zero. Slip = (tachometer rpm − calculated rpm) ÷ tachometer rpm. Use the true road speed from GPS and the real rolling diameter of the tire, or the error in those numbers ends up in the slip.

Top speed: the gearing limit and the real one

The Top speed tab gives the speed each gear reaches at the redline. In the tallest gear that is the gearing-limited top speed: the car cannot go faster without passing the redline, whatever the power. Every lower gear in the table shows where that gear tops out, which is the transmission speed calculator side of the tab.

It is rarely the speed a car actually reaches. Aerodynamic drag grows with the square of speed and the power needed to overcome it with the cube, so most cars run out of power before they can pull the redline in an overdrive top gear. The real top speed lands where the power reaching the wheels equals what drag and rolling resistance absorb, which takes the car's power, frontal area and shape, none of which a gearing calculation knows. Treat the figure as a ceiling and keep any run toward it on a closed track.

The rpm formulas

Every formula builds on the speed-to-rpm relationship used for gearing, with slip added where the engine and the transmission input turn at different speeds. None of them is empirical: the results are exact for the numbers you enter, and the uncertainty is in the inputs.

1. Overall ratio = transmission gear ratio × rear end gear ratio
2. RPM from the gearing = mph × overall ratio × 336.14 ÷ tire diameter (in)
3. Engine rpm = rpm from the gearing ÷ (1 − slip)
4. Speed at an rpm (mph) = rpm × (1 − slip) × tire diameter ÷ (overall ratio × 336.14)
5. RPM after an upshift = shift rpm × next gear ratio ÷ current gear ratio
6. RPM drop = shift rpm − rpm after the upshift

The 336.14 turns road speed into tire revolutions per minute: 63,360 inches in a mile, divided by 60 minutes in an hour and by π. The upshift formula needs neither the tire nor the rear gear, because road speed doesn't change during the shift and the rpm simply scales by the ratio of the two gears. That is why the drop in percent is the same whatever the shift rpm, and why a close-ratio gearbox keeps the engine in a narrower band.

Worked example

Three typical questions, worked out with the same functions that run the calculator.

Speed per 1,000 rpm for common setups

Speed per 1,000 rpm is the quickest way to read any setup: multiply it by the rpm in thousands to get road speed, or divide a road speed by it to get the rpm in thousands. The table works it out for common overall ratios and tire diameters. In a 1:1 top gear the overall ratio is simply the rear end ratio; in any other gear, multiply the two first.

With converter slip, multiply the speed in the table by (1 − slip), or divide the rpm by it. Taller tires and lower overall ratios give more speed per 1,000 rpm, which is a quieter cruise and a higher gearing-limited top speed, paid for with less pull in every gear.

Common mistakes

• Leaving out converter slip. An unlocked converter makes the engine turn faster than the gearing suggests. Enter the slip, or compare figures only once the converter has locked.
• Reading the top-speed figure as a promise. The gearing-limited speed ignores drag and power, and most cars never reach it in their top gear.
• Entering the gears out of order. The shift chart needs first gear first and each ratio lower than the one before; overdrive ratios go last.
• Forgetting tire growth at the top end. Drag slicks and other bias-ply tires grow taller at speed, so at the finish line the real rolling diameter can be larger than the one measured at rest, and the speed at a given rpm comes out higher than calculated.
• Using the size code as the tire diameter. The first number of a metric code is the width in millimeters. Convert the code with the tire size calculator first.
• Choosing a shift rpm without looking at the drop. The best upshift leaves the engine where it pulls harder in the next gear than it would by staying in the current one. Compare the rpm after each shift with the engine's power curve.
• Mixing up the overall ratio and the rear end ratio. In an overdrive the overall ratio is lower than the rear end ratio; in first gear it is several times higher.