Gear Ratio and RPM to Speed Calculator

How to use this tool

Pick what to calculate. Road speed from engine RPM and engine RPM at a road speed use one equation in opposite directions, so the second is the cruise RPM question. The speedometer mode compares two tyres, the bicycle mode takes chainring, cog, wheel and cadence, and the gear pair mode takes tooth counts, input speed, input torque and an efficiency. The table under the result lists every gear of an example six speed set. It is an illustration, so replace the ratios with your own.

The input people most often get wrong is the direction of the gear ratio. An overdrive of 0.75 means the engine turns 0.75 times for each turn of the driveshaft, and entering 1.33 makes the road speed 44% too low. Final drives stamped as tooth counts, such as 41:11, are accepted as they are. For tyres, type the whole code, such as 225/60R16 or LT265/70R17, or a plain diameter, never the rim size alone. Leave the rolling diameter at 100 unless you know your tyre rolls smaller.

What the calculation is doing

A tyre code gives the section width in millimetres, the aspect ratio (sidewall height as a percentage of the width) and the rim diameter in inches. Overall diameter = 2 × width × aspect ratio ÷ 100 + rim diameter × 25.4 mm, which is 676.4 mm or 26.63 in for 225/60R16. Wikipedia’s tyre code article gives the same formula and works 195/55R16 as 621 mm and 24.44 in, which the tool reproduces. Circumference is π times the diameter, and revolutions per mile is 63,360 ÷ the circumference in inches, 757 for this tyre.

The wheels turn at engine speed ÷ (gear ratio × final drive). Multiply by the circumference for distance per minute and convert: mph = wheel rpm × circumference in inches × 60 ÷ 63,360. Folding the constants together gives the formula parts retailers print, mph = rpm × diameter ÷ (gear ratio × final drive × 336). The 336 is 1056 ÷ π, where 1,056 is 63,360 ÷ 60 and the π absorbs the circumference. The exact value is 336.14, so rounding to 336 makes every answer 0.04% high, and the tool keeps the exact figure. The reverse mode solves the same equation for RPM.

For a bicycle, gear inches is the wheel diameter × chainring ÷ cog, as Sheldon Brown defines it, development is the wheel circumference × the same ratio, and speed is development × cadence. A gear pair has a ratio of driven teeth ÷ driver teeth: output speed is input speed ÷ ratio, and output torque is input torque × ratio × efficiency.

Why a lower ratio cuts cruise RPM and what it costs in torque

Ratios multiply down the drivetrain. Wikipedia’s gear ratio article gives the first gear of a Corvette C5 Z06, 2.97, with its 3.42 final drive as 10.16 to 1, about ten engine turns for each wheel turn. In the 0.80 gear of the example set the overall ratio is 2.84, and 70 mph needs 2,509 rpm against 3,137 in direct drive. That is 20% lower, because RPM at a fixed speed is proportional to the overall ratio, and a lower numerical final drive does the same to every gear at once.

The price is torque. A ratio divides speed and multiplies torque by the same factor, so power stays the same apart from losses. First gear in the example set has an overall ratio of 12.42, so the wheels see about 12 times the engine torque and turn 12 times slower. RoyMech quotes 98 to 99% for a single spur mesh, counting tooth friction only, and NASA’s tests found spur gears generally above 98% except at very low torque. Meshes in series multiply, so two at 98% leave 96%, and bearings, seals and oil churning cost more, which is why efficiency is an input.

The same scaling explains speedometers and bicycles. A speedometer counts wheel turns and multiplies by the circumference of the tyre it was set up for, so a taller tyre covers more road per turn than the dial assumes, and true speed exceeds the reading by the same percentage as the diameter grew. Bicycles use gear inches because a chain hides the wheel size: each gear becomes the diameter of a directly driven wheel that would go as far per pedal turn. A 34 × 34 is 26.4 gear inches, the wheel diameter itself, and a 50 × 11 is 119.9.

Cruise RPM for common tyres and final drives

The RPM at 70 mph in direct drive, a gear ratio of 1.00. For any other top gear, multiply by its ratio: a 0.75 overdrive cuts every figure by a quarter. Use the tool for 100 km/h.

The next table compares revolutions per mile calculated from the size code with the figures listed for the same sizes in a public tyre database, tiresize.com. They agree within one revolution per mile, because the database rounds its diameters. The bigger gap, between the code and what particular tyres do under load, is covered under the mistakes below.

A worked example you can check on paper

The defaults: 2,500 rpm, gear ratio 1.00, final drive 3.55 and 225/60R16 tyres. Sidewall = 225 × 60 ÷ 100 = 135 mm. Diameter = 2 × 135 + 16 × 25.4 = 676.4 mm = 26.63 in. Circumference = π × 26.63 = 83.66 in. Overall ratio = 1.00 × 3.55 = 3.55, so the wheels turn at 2,500 ÷ 3.55 = 704.2 rpm. Speed = 704.2 × 83.66 × 60 ÷ 63,360 = 55.79 mph, or 89.8 km/h.

Closed form as a check: 2,500 × 26.63 ÷ (3.55 × 336.14) = 55.79 mph. Turned round, cruising at 70 mph needs 3,137 rpm, and at 100 km/h it needs 2,784 rpm. Now the speedometer: changing from 225/45R17 to 235/40R18 makes the diameter 25.40 ÷ 24.97 = 1.0172 times the old one, so 60 mph shown is 60 × 1.0172 = 61.0 mph.

Mistakes that catch people out

Using the rim size as the tyre diameter. The 16 in 225/60R16 is the wheel, not the tyre. The tyre is 26.63 in tall. Enter the full code or the overall diameter and the tool does the rest.

Reading the gear ratio backwards. Ratios below 1.00 are overdrives, where the engine turns slower than the shaft it drives. Enter 0.75, not 1.33, or the answer is out by 44% for speed and 78% for RPM.

Treating the code as the rolling diameter. A loaded tyre rolls a little smaller than its nominal size. For 225/60R16 the code gives 757 revolutions per mile, while the same database lists 758 for the size in general but 779, 781 and 782 on the pages of three specific tyres, about 2.9 to 3.3% more. Enter 97 in the rolling diameter box to match them.

Forgetting a second reduction. A transfer case, a portal axle or a hub reduction multiplies into the overall ratio. Enter the product in the final drive box, or the RPM will come out too low by that factor.

Assuming all 622 wheels roll the same. A 700 x 23 and a 700 x 50 share a rim, but Sheldon Brown lists their rolling circumferences as 2,097 and 2,293 mm, 9.3% apart. Pick the tyre width in the wheel list, or measure your own wheel and use the custom diameter.

Popular calculations

Each opens the calculator with those figures filled in, and everything can be changed once it is open.

Cruise RPM at 100 km/h and 70 mph

Road speed at redline style and cruising engine speeds

Speedometer error after a tyre change

Bicycle gear inches and development

Gear pair examples

How this was checked

Tyre sizes were compared with published figures. The tool gives 621 mm and 24.44 in for 195/55R16, matching the worked example in Wikipedia’s tyre code article, and 25.9, 25.0 and 25.4 in for 225/50R17, 225/45R17 and 235/40R18, matching America’s Tire. Studebaker Info calculates 225/60R16 as 26.62 in and 757 revolutions per mile, and the tool gives 26.63 in and 757.3. An online calculator prints 784.16 revolutions per mile for 245/40R18 with π taken as 3.14, and the tool gives 784.2 with the full value. The four sizes in the reference table land within one revolution per mile of the tyre database. The speed formula was checked against a worked example from Firgelli, 3,000 rpm with a 3.73 ratio and 28 in tyres: the page prints 66.9 mph and exact arithmetic gives 67.0, so the page truncated.

Independent routes then tested the engine. On 5,000 random inputs, a chain of angular velocities, engine radians per second to wheel radians per second to metres per second, matched the closed form to within one part in a quadrillion. The reverse mode returned the starting RPM on 4,000 random cases in both unit systems, and unit conversions round tripped. On the bike side, Sheldon Brown prints 8.64 m for a 52/13 on a 622 mm rim with a 33 mm tyre and 1.78 m for a 24/28 on 559 mm with 51 mm. The tool gives 8.646 and 1.780, so the first rounds to 8.65 and his figure sits 0.006 m low, a rounding difference. Wikipedia’s 26 inch wheel gives 52, 37 and 113 gear inches for 48/24, 48/34 and 48/11, and the tool returns 52.0, 36.7 and 113.5. For gear pairs, Wikipedia’s 13 to 42 train has a ratio of 3.23 (tool 3.231), and power out equalled power in times efficiency on 3,000 random cases. All 58 checks in the verification script pass.

Where sources disagree, both are shown. Sheldon Brown says a road tyre rolls about 1% smaller than its nominal diameter, and his table gives the 700 x 25 circumference as 2,105 mm. For cars, the published revolutions per mile of three 225/60R16 tyres, 779, 781 and 782, imply a rolling diameter of 96.8 to 97.2% of nominal, and Tire Rack explains why: the tread and sidewall deflect under load, so revolutions per mile cannot come from simple arithmetic. America’s Tire rounds the 225/45R17 to 235/40R18 change to about 1.6%, where exact codes give 1.72%. The exact 25.4 mm inch and 1.609344 km mile come from NIST SP 811, and the gear efficiency figures from RoyMech and NASA TM 81426.

Common questions

How do I calculate engine RPM from road speed?

Turn the speed into wheel turns per minute, then multiply by the overall ratio. In mph and inches, RPM = speed × gear ratio × final drive × 336.14 ÷ tyre diameter. For 70 mph in direct drive with a 3.55 final drive on 26.63 in tyres that is 3,137 rpm, and a 0.75 overdrive brings it to 2,353 rpm.

Where does the 336 in the speed formula come from?

It is 1056 ÷ π. One mile per hour is 63,360 ÷ 60 = 1,056 inches per minute, and a tyre covers π times its diameter per turn. Written formulas round 336.14 to 336, which makes every answer 0.04% high. In km/h with the diameter in millimetres the constant is 1,000,000 ÷ (60 π) = 5,305.2.

How much will bigger tyres throw off my speedometer?

True speed is the reading times the new diameter divided by the old. Changing from 225/45R17 (24.97 in) to 235/40R18 (25.40 in) makes the tyre 1.72% taller, so 60 mph on the dial is 61.0 mph, and every 100 miles on the odometer is really 101.7. America’s Tire suggests keeping overall diameter within about 3% of the original. Speedometers are also built to read high on purpose: under UN Regulation 39 the indicated speed may never be below the true speed and may reach 110% of it plus 4 km/h at type approval. Wear works the other way, since going from 8 mm to 1.6 mm of tread shrinks a 620 mm tyre by about 2%. Treat the result as a planning estimate and check it against GPS. It is not a legal speedometer calibration.

Does a lower numerical ratio always mean better fuel use?

It always means a lower engine speed at the same road speed. It also asks the engine to make the same power at lower speed, which needs more torque and a wider throttle opening. Whether the trade helps depends on the engine, the load and the gearbox, so treat the RPM figure as a planning input and not as a fuel promise.

What are gear inches and development, and what cadence should I enter?

Gear inches is the size of a wheel that would go as far per pedal turn if it were driven directly. Development is the distance covered per crank turn, and it equals gear inches times 0.0254π, about 0.0798, in metres. Wikipedia lists 60 to 80 rpm as typical for recreational riders and 90 to 100 for racers, so the default is 90. Enter your own from a cycle computer.

How much torque does a gear pair give, and what efficiency should I enter?

Torque is multiplied by the ratio of driven to driver teeth and by the efficiency, while speed is divided by the ratio. A 20 tooth driver on a 60 tooth driven gear at 98% turns 1,800 rpm into 600 rpm and 10 lb ft into 29.4 lb ft. Take 98% as the ceiling for one spur mesh and enter a lower figure once bearings, seals and oil are counted.

Related Calculators and Reference

• Speed, Distance and Time Calculator: turn the road speed you found into a trip time or a distance.
• Speed Converter: switch a speed between km/h and mph when a source quotes the other unit.
• Torque Converter: move the gear pair torque figures between N m and lb ft.
• Gas Cost Calculator: price a trip once you know the speed you will hold.
• Kinetic Energy Calculator: see the energy a vehicle carries at the speed you just worked out.
• Engine Compression Ratio and Displacement Calculator: displacement and compression ratio from bore, stroke and chamber volume.
• Tire Size Calculator: the tire diameter and revolutions per mile behind the speed, and what a swap does to the speedometer.
• Wheel Offset Calculator: offset and backspacing for the wheels that carry the tires.
• Horsepower Calculator: estimate the power at the rpm a gear puts the engine at.
• Sheldon Brown, gear inches, development and gain ratio: the definitions and worked examples behind the bicycle mode.