Gear Inch and Shifting Pattern Calculator

The Cycling Calculator came on line 10 years ago February 1996 as a simple program to calculate gear inch and shifting patterns in multispeed bicycles. Since then several features have been added.

Ten Chainrings

Ten chainrings are now available for selection on the main forms page. These additional chainrings (four thru ten) exist mainly for the Single-speed option available on the forms page.

Multi-speed and Single-speed

You gear selections can be processed either as a multispeed setup or as a fixed gear singlespeed setup. Multispeed treats the selected values as an individual multispeed bicycle; a single crank with one or more chainrings and a single freewheel cluster with one or more cogs.
Singlespeed treats the selected values as one or more fixed speed bicycles. When selecting values for singlespeed processing one must choose matched pairs on the forms page. For more details on this option review the Multispeed-singlespeed documentation.

Unit of Measure

The output display can be either in the U.S. unit of measure (inches/feet/miles) or in the Metric unit of measure (centimeters/meters/kilometers).

Pop and Push the Stack

At the bottom of the display page are checkbox buttons for each of the chainring & freewheel combinations you have selected. These checkboxes represent the CRxFW combinations you can omit from the recalculations. Lets say you want to remove a repeat or near repeat value, or drop the 42x12 & 53x24 combinations; the big to big and small to small. Simply select the checkboxes for each of the CRxFW values you want to delete from the original chart, then recalculate. The new page will display your CRxFW arrangement minus those checked values.
The omited CRxFW values will be popped from the stack and displayed below the chart. Now, if you want to add them back, simply check the appropiate checkbox to add back the previously deleted values.

Cadence

Once on the display page users have the option to view the cadance MPH/KPH calculations for their selected gearing setup.

Calculations

The following calculations are performed on the supplied data:

For the U.S. version:
  1. GearInches = (ChainRing / FreeWheel) * WheelDiameter
  2. DistanceInches = GearInches * PI
  3. DistanceFeet = DistanceInches / 12
  4. PedalRotationsPerMile = 5280 / DistanceFeet
For the Metric version:
  1. Gear_millimeters = (ChainRing / FreeWheel) * WheelDiameter_in_millimeters
  2. Gear_centimeters = Gear_millimeters / 10
  3. Distance_millimeters = Gear_millimeters * PI
  4. Distance_centimeters = Distance_millimeters / 10
  5. Distance_meters = Distance_millimeters / 100
  6. PedalRotationsPerKilometer = 1000 / Distance_meters

Before displaying the data this program will sort the GearInch or Gear_millimeter values, then continue on with the other calculations. The final results are then displayed showing you the sequential shifting order of your "Chainring + FreeWheel + Wheel_Diameter" combination.

By inspecting the GearInch & DistanceInch columns, or the GearInch & Distance_centimeter in the Metric version, one can easily determine where the repeats, or near repeats occur. Further comparisons are displayed in the diff and GIdf - GCMdf columns. The diff value represents the difference between the present chainring x freewheel combination, and the next sequential chainring x freewheel combination. The GIdf - GCMdf column shows the percentage of increase between the current chainring x freewheel combination and the next sequential chainring x freewheel combination.

With this information you can now fine-tune your shifting skills, making the most use of your current chainring & freewheel combination.

Interpreting the Data

SP
The sequential "Shifting Pattern" of your Chainring x Freewheel combination
( 1st gear, 2nd gear, 3rd gear,... etc )

CRxFW
"ChainRing x FreeWheel".

GI
"Gear Inches". (U.S. Version)

GCM
"Gear Centimeters". (Metric Version)

GIdf
Percentage of increase between the present GI value and the next sequential GI value. (U.S. Version)

GCMdf
Percentage of increase between the present GCM value and the next sequential GCM value. (Metric Version)

DI
The distance in INCHES traveled in a single pedal rotation. (U.S. Version)

CM
The distance in CENTIMETERS traveled in a single pedal rotation. (Metric Version)

diff
The difference in either INCHES or CENTIMETERS between the present DI or CM value and the next sequential DI or CM value.
The diff values are displayed in inches, with a decimal remainder in the U.S. version or in centimeters in the Metric version.

DF
The distance in FEET traveled in a single pedal rotation, displayed as "FEET : INCHES . Decimal_Remainder". (U.S. Version)

M
The distance in METERS traveled in a single pedal rotation. (Metric Version)

PRPM
"Pedal Rotations Per Mile". (U.S. Version)

PRPK
"Pedal Rotations Per Kilometer". (Metric Version)

RT
"Gear Ratios".

Output Display

Multispeed

Below is the output from a 42 x 53 chainring and 24-22-20-18-16-14 freewheel combination, calculated in multispeed mode and displayed in inches/feet: 
 SP        Shifting Pattern
 CRxFW     ChainRing x FreeWheel
 GI        Gear Inches
 GIdf      Percentage of increase between present GI value and the
           next sequential GI value.
 DI        Distance traveled in INCHES in a single pedal rotation
 diff      Difference in INCHES between the present DI value and 
           the next sequential DI value. 
 DF        Distance traveled in FEET in a single pedal rotation
           displayed as FEET' INCHES.decimal_remainder"
 PRPM      Pedal Rotations Per Mile
 RT        Gear Ratios

 Wheel Diameter: 26.60 inches
 Gears: 42/53   14-16-18-20-22-24
---------------------------------------------------------------------------
 SP  CRxFW    GI      GIdf      DI      diff      DF        PRPM      RT
---------------------------------------------------------------------------
 1>  42x24   46.55    9.09%   146.24   13.29   12' 2.24"   433.26   1:1.75
 2>  42x22   50.78   10.00%   159.54   15.95   13' 3.54"   397.15   1:1.91
 3>  42x20   55.86    5.16%   175.49    9.05   14' 7.49"   361.05   1:2.10
 4>  53x24   58.74    5.66%   184.54   10.45   15' 4.54"   343.34   1:2.21
 5>  42x18   62.07    3.25%   194.99    6.33   16' 2.99"   324.94   1:2.33
 6>  53x22   64.08    8.96%   201.32   18.04   16' 9.32"   314.72   1:2.41
 7>  42x16   69.83    0.95%   219.36    2.09   18' 3.36"   288.84   1:2.62
 8>  53x20   70.49   11.11%   221.45   24.61   18' 5.45"   286.11   1:2.65
 9>  53x18   78.32    1.89%   246.06    4.64   20' 6.06"   257.50   1:2.94
10>  42x14   79.80   10.42%   250.70   26.11   20'10.70"   252.73   1:3.00
11>  53x16   88.11   14.29%   276.81   39.54   23' 0.81"   228.89   1:3.31
12>  53x14  100.70    0.00%   316.36    0.00   26' 4.36"   200.28   1:3.79
---------------------------------------------------------------------------
 SP  CRxFW    GI      GIdf      DI      diff      DF        PRPM      RT
---------------------------------------------------------------------------

In the diff column the " 6.33 " on line 5 shows the difference between the DI value on 5 and the DI value on 6. This means there is a difference of 6.33 INCHES (6&5/16th inch) of ground covered in a single pedal rotation between the chainring & freewheel combinations of 42x18 and 53x22 ( on a 26.60 inch wheel ). 

 SP  CRxFW    GI      GIdf      DI      diff      DF        PRPM      RT
 5>  42x18   62.07    3.25%   194.99    6.33   16' 2.99"   324.94   1:2.33
 6>  53x22   64.08    8.96%   201.32   18.04   16' 9.32"   314.72   1:2.41
 7>  42x16   69.83    0.95%   219.36    2.09   18' 3.36"   288.84   1:2.62

While in a 42x16 combination, the Distance in Feet traveled in a single pedal rotation is 18 feet, 3&3/8 inches, displayed as 18' 3.36" (on a 26.60 inch wheel).

Below is the same gearing combination as above, calculated in multispeed mode and displayed in centimeters/meters:
 SP        Shifting Pattern
 CRxFW     ChainRing x FreeWheel
 GCM       Gear Centimeters
 GCMdf     Percentage of increase between present GCM value and the
           next sequential GCM value.
 CM        Distance traveled in CENTIMETERS in a single pedal rotation
 diff      Difference in CENTIMETERS between the present CM value
           and the next sequential CM value.
 M         Distance traveled in METERS in a single pedal rotation
 PRPK      Pedal Rotations Per Kilometer
 RT        Gear Ratios

 Wheel Diameter: 678mm
 Gears: 42/53   14-16-18-20-22-24
---------------------------------------------------------------------------
 SP  CRxFW    GCM     GCMdf      CM      diff       M      PRPK       RT
---------------------------------------------------------------------------
 1>  42x24  118.65    9.09%    372.75    33.89    3.73    268.28   1:1.75
 2>  42x22  129.44   10.00%    406.64    40.66    4.07    245.92   1:1.91
 3>  42x20  142.38    5.16%    447.30    23.07    4.47    223.56   1:2.10
 4>  53x24  149.72    5.66%    470.37    26.62    4.70    212.60   1:2.21
 5>  42x18  158.20    3.25%    497.00    16.14    4.97    201.21   1:2.33
 6>  53x22  163.34    8.96%    513.14    45.99    5.13    194.88   1:2.41
 7>  42x16  177.97    0.95%    559.12     5.32    5.59    178.85   1:2.62
 8>  53x20  179.67   11.11%    564.45    62.72    5.64    177.16   1:2.65
 9>  53x18  199.63    1.89%    627.17    11.83    6.27    159.45   1:2.94
10>  42x14  203.40   10.42%    639.00    66.56    6.39    156.49   1:3.00
11>  53x16  224.59   14.29%    705.56   100.79    7.06    141.73   1:3.31
12>  53x14  256.67    0.00%    806.36     0.00    8.06    124.01   1:3.79
---------------------------------------------------------------------------
 SP  CRxFW    GCM     GCMdf      CM      diff       M      PRPK      RT
---------------------------------------------------------------------------
In the diff column the "16.14" on line 5 shows the difference between the CM value on 5 and the CM value on 6. This means there is a difference of 16.14 CENTIMETERS of ground covered in a single pedal rotation between the chainring & freewheel combinations of 42x18 and 53x22 ( on a wheel with a diameter of 678 millimeters ). 

 SP  CRxFW    GCM     GCMdf      CM      diff       M      PRPK       RT
 5>  42x18  158.20    3.25%    497.00    16.14    4.97    201.21   1:2.33
 6>  53x22  163.34    8.96%    513.14    45.99    5.13    194.88   1:2.41
 7>  42x16  177.97    0.95%    559.12     5.32    5.59    178.85   1:2.62

Singlespeed

In this next example all ten chainring and freewheel boxes from the forms page have been selected with valid (non-zero) values. The "Gears" line now shows the ten individual fixed speed combinations. Had Multispeed mode been chosen for those ten chainrings and freewheels the program would have displayed 100 gearing combinations instead of 10. 
 SP        Shifting Pattern
 CRxFW     ChainRing x FreeWheel
 GI        Gear Inches
 GIdf      Percentage of increase between present GI value and the
           next sequential GI value.
 DI        Distance traveled in INCHES in a single pedal rotation
 diff      Difference in INCHES between the present DI value and 
           the next sequential DI value. 
 DF        Distance traveled in FEET in a single pedal rotation
           displayed as FEET' INCHES.decimal_remainder"
 PRPM      Pedal Rotations Per Mile
 RT        Gear Ratios

 Wheel Diameter: 26.60 inches
 Gears: 53x20 50x18 53x19 52x18 53x18 48x16 52x17 50x16 52x16 48x14 
---------------------------------------------------------------------------
 SP  CRxFW    GI      GIdf      DI      diff      DF        PRPM      RT
---------------------------------------------------------------------------
 1>  53x20   70.49    4.82%   221.45   10.68   18' 5.45"   286.11   1:2.65
 2>  50x18   73.89    0.42%   232.13    0.98   19' 4.13"   272.95   1:2.78
 3>  53x19   74.20    3.56%   233.11    8.31   19' 5.11"   271.81   1:2.79
 4>  52x18   76.84    1.92%   241.41    4.64   20' 1.41"   262.45   1:2.89
 5>  53x18   78.32    1.89%   246.06    4.64   20' 6.06"   257.50   1:2.94
 6>  48x16   79.80    1.96%   250.70    4.92   20'10.70"   252.73   1:3.00
 7>  52x17   81.36    2.16%   255.61    5.53   21' 3.61"   247.87   1:3.06
 8>  50x16   83.12    4.00%   261.14   10.45   21' 9.14"   242.62   1:3.12
 9>  52x16   86.45    5.49%   271.59   14.92   22' 7.59"   233.29   1:3.25
10>  48x14   91.20    0.00%   286.51    0.00   23'10.51"   221.14   1:3.43
---------------------------------------------------------------------------
 SP  CRxFW    GI      GIdf      DI      diff      DF        PRPM      RT
---------------------------------------------------------------------------

Cadence

The cadance display shows the user how many miles per hour or kilometers per hour one would go in a certain chainring & freewheel combination. The Revolution Per Minute values start at 40 and increment by 5 up till 175. Below we have one line showing a 42x24 setup (with a 26.70 inch wheel). Next in this line is the corresponding Gear Inch value for that setup. What follows on that line is the Miles Per Hour (MPH) values for this 42x24 combination at RPM's of 40, 45, 50, 55, 60, 65 and 70. The lines are read left to right. 
 SP CRxFW     GI |        40      45      50      55      60      65      70 
 1> 42x24   46.73 MPH:   5.56    6.26    6.95    7.65    8.34    9.04    9.73
In this 42x24 combination (with a 26.70 inch wheel) one would be traveling at 9.04 miles per hour while spinning at 65 RPM. Below is a complete sample display from the Cadance program: 
 SP	Shifting Pattern
 CRxFW	Chainring x FreeWheel
 GI	Gear Inches
 MPH	Miles Per Hour

 Wheel Diameter: 26.70 inches
 Gears: 42/53   14-16-18-20-22-24
-----------------------------------------------------------------------------
                 |                 REVOLUTIONS  PER  MINUTE 
 SP CRxFW     GI |        40      45      50      55      60      65      70 
-----------------------------------------------------------------------------
 1> 42x24   46.73 MPH:   5.56    6.26    6.95    7.65    8.34    9.04    9.73
 2> 42x22   50.97 MPH:   6.07    6.82    7.58    8.34    9.10    9.86   10.62
 3> 42x20   56.07 MPH:   6.67    7.51    8.34    9.17   10.01   10.84   11.68
 4> 53x24   58.96 MPH:   7.02    7.89    8.77    9.65   10.52   11.40   12.28
 5> 42x18   62.30 MPH:   7.41    8.34    9.27   10.19   11.12   12.05   12.97
 6> 53x22   64.32 MPH:   7.65    8.61    9.57   10.52   11.48   12.44   13.40
 7> 42x16   70.09 MPH:   8.34    9.38   10.43   11.47   12.51   13.55   14.60
 8> 53x20   70.75 MPH:   8.42    9.47   10.52   11.58   12.63   13.68   14.73
 9> 53x18   78.62 MPH:   9.36   10.52   11.69   12.86   14.03   15.20   16.37
10> 42x14   80.10 MPH:   9.53   10.72   11.91   13.11   14.30   15.49   16.68
11> 53x16   88.44 MPH:  10.52   11.84   13.16   14.47   15.79   17.10   18.42
12> 53x14  101.08 MPH:  12.03   13.53   15.04   16.54   18.04   19.55   21.05

-----------------------------------------------------------------------------
                 |                 REVOLUTIONS  PER  MINUTE 
 SP CRxFW     GI |        75      80      85      90      95     100     105 
-----------------------------------------------------------------------------
 1> 42x24   46.73 MPH:  10.43   11.12   11.82   12.51   13.21   13.90   14.60
 2> 42x22   50.97 MPH:  11.37   12.13   12.89   13.65   14.41   15.16   15.92
 3> 42x20   56.07 MPH:  12.51   13.34   14.18   15.01   15.85   16.68   17.51
 4> 53x24   58.96 MPH:  13.16   14.03   14.91   15.79   16.66   17.54   18.42
 5> 42x18   62.30 MPH:  13.90   14.83   15.75   16.68   17.61   18.53   19.46
 6> 53x22   64.32 MPH:  14.35   15.31   16.27   17.22   18.18   19.14   20.09
 7> 42x16   70.09 MPH:  15.64   16.68   17.72   18.77   19.81   20.85   21.89
 8> 53x20   70.75 MPH:  15.79   16.84   17.89   18.94   20.00   21.05   22.10
 9> 53x18   78.62 MPH:  17.54   18.71   19.88   21.05   22.22   23.39   24.56
10> 42x14   80.10 MPH:  17.87   19.06   20.26   21.45   22.64   23.83   25.02
11> 53x16   88.44 MPH:  19.73   21.05   22.37   23.68   25.00   26.31   27.63
12> 53x14  101.08 MPH:  22.55   24.06   25.56   27.06   28.57   30.07   31.57

-----------------------------------------------------------------------------
                 |                 REVOLUTIONS  PER  MINUTE 
 SP CRxFW     GI |       110     115     120     125     130     135     140 
-----------------------------------------------------------------------------
 1> 42x24   46.73 MPH:  15.29   15.99   16.68   17.38   18.07   18.77   19.46
 2> 42x22   50.97 MPH:  16.68   17.44   18.20   18.96   19.71   20.47   21.23
 3> 42x20   56.07 MPH:  18.35   19.18   20.02   20.85   21.69   22.52   23.35
 4> 53x24   58.96 MPH:  19.30   20.17   21.05   21.93   22.80   23.68   24.56
 5> 42x18   62.30 MPH:  20.39   21.31   22.24   23.17   24.09   25.02   25.95
 6> 53x22   64.32 MPH:  21.05   22.01   22.96   23.92   24.88   25.83   26.79
 7> 42x16   70.09 MPH:  22.94   23.98   25.02   26.06   27.11   28.15   29.19
 8> 53x20   70.75 MPH:  23.15   24.21   25.26   26.31   27.36   28.42   29.47
 9> 53x18   78.62 MPH:  25.73   26.90   28.07   29.24   30.40   31.57   32.74
10> 42x14   80.10 MPH:  26.21   27.40   28.60   29.79   30.98   32.17   33.36
11> 53x16   88.44 MPH:  28.94   30.26   31.57   32.89   34.21   35.52   36.84
12> 53x14  101.08 MPH:  33.08   34.58   36.08   37.59   39.09   40.60   42.10

-----------------------------------------------------------------------------
                 |                 REVOLUTIONS  PER  MINUTE 
 SP CRxFW     GI |       145     150     155     160     165     170     175 
-----------------------------------------------------------------------------
 1> 42x24   46.73 MPH:  20.16   20.85   21.55   22.24   22.94   23.63   24.33
 2> 42x22   50.97 MPH:  21.99   22.75   23.50   24.26   25.02   25.78   26.54
 3> 42x20   56.07 MPH:  24.19   25.02   25.86   26.69   27.52   28.36   29.19
 4> 53x24   58.96 MPH:  25.43   26.31   27.19   28.07   28.94   29.82   30.70
 5> 42x18   62.30 MPH:  26.87   27.80   28.73   29.65   30.58   31.51   32.43
 6> 53x22   64.32 MPH:  27.75   28.70   29.66   30.62   31.57   32.53   33.49
 7> 42x16   70.09 MPH:  30.23   31.28   32.32   33.36   34.40   35.45   36.49
 8> 53x20   70.75 MPH:  30.52   31.57   32.63   33.68   34.73   35.78   36.84
 9> 53x18   78.62 MPH:  33.91   35.08   36.25   37.42   38.59   39.76   40.93
10> 42x14   80.10 MPH:  34.55   35.74   36.94   38.13   39.32   40.51   41.70
11> 53x16   88.44 MPH:  38.15   39.47   40.78   42.10   43.41   44.73   46.05
12> 53x14  101.08 MPH:  43.60   45.11   46.61   48.11   49.62   51.12   52.62
-----------------------------------------------------------------------------

jbarrm at panix.com