SOLVETUTORMATH SOLVER

Instrument MI-06-224 · Everyday life

RPM Calculator

Enter engine RPM, overall gear ratio, and tire diameter, and this instrument returns the road speed that combination produces — the calculation a speedometer performs mechanically.

Instrument MI-06-224
Sheet 1 OF 1
Rev A
Verified
Type 06 — Motion SER. 2026-06224

Vehicle speed (mph)

68.85

speed = (engine RPM / gear ratio) x tire diameter x pi x 60 / 63,360

The working Every figure verified twice
  1. speedMph = 3000 ⁄ 3.5·27·π·60 ⁄ 63360 = 68.85
Worksheet log
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How this instrument works

A car's speedometer doesn't measure road speed directly — it counts wheel revolutions and converts that count into mph using two fixed numbers: the tire's rolling diameter and the vehicle's overall gear ratio. Engine RPM divided by the overall gear ratio gives wheel RPM (how many times the wheels themselves turn per minute), because the transmission and differential each step the engine's spin down before it reaches the wheels.

Overall gear ratio is a single number that already combines two separate ratios: the transmission's gear ratio in whatever gear you're in, multiplied by the differential's final-drive ratio. A 2004 Corvette in first gear, for example, has roughly a 2.97:1 transmission ratio and a 3.42:1 differential ratio, multiplying to about 10.16:1 overall — meaning the engine spins 10.16 times for every single wheel revolution. Enter that combined figure here, not the transmission ratio alone.

Once wheel RPM is known, multiplying by the tire's circumference (diameter × π) gives the distance covered per minute, and a fixed conversion (63,360 inches per mile, 60 minutes per hour) turns that into mph. This is exactly the arithmetic a mechanical speedometer cable performs, and it's also what riders informally call the '336 constant' shortcut — MPH ≈ (RPM × tire diameter) ÷ (gear ratio × 336), where 336 collapses the π and unit-conversion terms into one number.

vmph=RPMG×D×π×6063,360v_{mph} = \dfrac{RPM}{G}\times D \times \pi \times \dfrac{60}{63{,}360}
RPM — engine speed. G — overall gear ratio (transmission ratio × differential ratio). D — tire diameter in inches. 63,360 converts inches to miles; 60 converts minutes to hours.
  • Find your engine RPM — read it off a tachometer, or use a target RPM from a spec sheet or dyno chart.
  • Enter your vehicle's overall gear ratio: transmission ratio (in the gear you're checking) × differential ratio, multiplied together.
  • Enter tire diameter in inches — the tire's full rolling diameter, not its width or rim size (check the sidewall code or measure directly).
  • Read Vehicle speed (mph) — the road speed that RPM produces in that gear with that tire.
  • Change gear ratio or tire size and recompute to see how taller gearing or larger tires shift top speed at the same RPM.

Worked example — cruising at 3,000 RPM in overdrive

A car turning 3,000 engine RPM through a 3.5:1 overall gear ratio (a typical combined transmission-and-differential figure for a highway gear) on 27-inch-diameter tires: wheel RPM = 3,000 ÷ 3.5 = 857.14. Multiplying by tire diameter, π, and the inch-to-mile-per-hour conversion factor gives speed = 857.14 × 27 × π × 60 ÷ 63,360 ≈ 68.85 mph.

That's a believable highway cruising speed for a car geared this way — and it cross-checks against the shortcut '336 constant' formula mechanics use in their heads: MPH ≈ (3,000 × 27) ÷ (3.5 × 336.13) ≈ 68.85 mph, the same answer from a rearranged version of the same physics.

Questions

What exactly is "overall gear ratio" here — transmission or differential?

Both, multiplied together. The transmission ratio (which gear you're in) and the differential/final-drive ratio each step down engine speed before it reaches the wheels, and their combined effect is the product of the two numbers. A 3rd gear ratio of 1.4:1 with a 3.55:1 differential gives an overall ratio of 1.4 × 3.55 = 4.97:1 — that combined figure is what this calculator wants, not either number alone.

Why does a numerically lower gear ratio mean higher speed at the same RPM?

Because RPM is divided by gear ratio to get wheel RPM. A "taller" gear (a lower numerical ratio, like 3.08:1 versus 4.10:1) means the engine turns fewer times per wheel revolution, so the same engine RPM pushes the car further per minute — hence a higher road speed. This is why highway "overdrive" gears use low numerical ratios and low first gears use high ones for torque instead of speed.

Where do I find my vehicle's differential (axle) ratio?

Common sources are a build sticker in the driver's door jamb, an RPO code on GM vehicles, a tag riveted to the axle housing itself, or the manufacturer's specification sheet for your exact trim and engine/transmission combination — axle ratio often varies between otherwise-identical trims, so match it to your specific vehicle rather than assuming a generic figure.

Does "tire diameter" mean width or overall rolling diameter?

Overall rolling diameter — the full height of the tire from the ground to the top, not the width printed first in a tire size code (like the 225 in 225/50R17). To get diameter from a tire code: rim diameter + 2 × (section width × aspect ratio ÷ 100), converted from millimeters to inches, or simply measure a mounted tire directly.

Is this the same as the "336 constant" formula some mechanics use?

Yes — MPH ≈ (RPM × tire diameter) ÷ (gear ratio × 336.13) is an algebraically rearranged version of the same wheel-revolution physics, where 336.13 absorbs the π and inches-per-mile-per-hour conversion terms into a single constant. Both forms give the same answer; this calculator uses the unrolled version so each conversion step stays visible.

References