← All tools

Gear Ratio Calculator

Work out what a pair of gears does to your speed and torque, and how far apart to mount them.

Inputs

The gear the power comes from.

The gear the power goes to.

Results

Gear ratio

—

Written as driven : driving.

In lowest terms

—

Wheel speed

—

Relative to motor speed.

Wheel torque

—

Relative to motor torque.

Center distance

—in

How far apart to mount the two shafts.

That is this many holes apart

—

Watch them turn

Watch them turn
0°

Both gears at their real sizes, the right distance apart, with a mark on each so you can follow it round. Turn the driving gear and watch two things: the driven gear goes the other way, and it goes round a different number of times. That second thing is the gear ratio.

When you would use this

  1. Our drive is too slow and we want to know what to change.

    Try a different pair here. The speed multiplier tells you what you gain, and the torque multiplier tells you what you give up. There is no pair that improves both.

  2. We cannot get the gears to mesh properly.

    Check the center distance and whether it lands on a whole number of holes. If it does not, the two gears are from different families and cannot mount on standard holes at all, however you angle the plate.

  3. Our motors keep stalling on the lift.

    More reduction means more torque at the output. Try a taller ratio here, then check it against the stall calculator to see whether it brings you back inside a safe fraction of stall.

How this is calculated

A gear pair trades speed for torque. Nothing is gained on balance. Whatever you multiply the torque by, you divide the speed by.

ratio = driven teeth ÷ driving teeth speed = motor speed ÷ ratio torque = motor torque × ratio

A reduction (ratio above 1) gives a slower, stronger drive that's harder to push around. An overdrive (ratio below 1) gives a faster drive with less pushing power. Neither one is correct. It depends on whether your game is won by speed or by contact.

Where to mount them

VEX spur gears are 24 diametral pitch, so a gear's pitch diameter in inches is its tooth count divided by 24. Two gears mesh when their shafts sit half the sum of those diameters apart:

center distance = (driving teeth + driven teeth) ÷ 48 inches

Because VEX structure has holes every 0.5", that distance has to land on the grid. It always does. Every standard VEX spur gear pair lands exactly on a hole. The four sizes are 12, 36, 60 and 84, all multiples of 12 offset the same way, so any pair sums to a multiple of 24 and the center distance works out to a whole number of holes. You can't pick a legal VEX spur pair that won't mesh on standard holes.

Direction

Two meshing gears turn in opposite directions. If that's a problem, put a third gear between them. An idler flips the direction back without touching the ratio, because its tooth count cancels out of the sum.

Sources & assumptions

Tooth counts are VEX's four published spur gear sizes. The 24 diametral pitch figure is derived rather than published: it's the value consistent with both VEX's gear dimensions and the 0.5" hole spacing, and it reproduces the center distances teams measure in practice.

Assumes a simple two-gear external mesh. Compound gear trains, where two gears lock on one shaft, multiply their ratios together. Run each stage through this calculator and multiply the results.

Every source the site uses, and when it was checked

Save this run, and compare

Keeps what is on screen so you can change something and see both sides of the change. Saved in this browser only, never uploaded.

Make a notebook page

Turns this calculation into a dated engineering notebook page: the setup, data, results, figures, working and sources, numbered and cited. You add the goal, the decision and the reflection in your own words, plus photos and sketches. Print it, paste it into Google Docs, or download a Word file or slides.

My notebook

Notebook page

More
Open My notebook

    This page

    Our own layouts

    A layout remembers how a page is set up: its type, its system, which parts print and which of your tables it uses. It never remembers a word, a number or a photo.

    Your team kept on this device
    Add someone to the team list
    Your words never written for you

    These are the parts a judge or teacher reads to see your thinking, so the page leaves them to you. Leave a box empty to get lined space for writing by hand. Start lines with "- " for a list. The notes under each box only count and point things out; they never change what you wrote.

    Rough notes

    Rough notes

    Rough notes

    Rough notes

    Rough notes

    Rough notes

    Rough notes

    Rough notes

    Rough notes

    The word counts can be measured against a target your team sets on My notebook. The reading level is Flesch-Kincaid grade level = 0.39 × (words ÷ sentences) + 11.8 × (syllables ÷ words) − 15.59. Syllables are counted by vowel groups, so the grade is an estimate of the school year the writing reads at. It says nothing about whether the writing is any good.

    One part at a time, with a clock. At the end of practice, while you remember it.
    How you tested your details

    Fill in what applies. These print as a small table under the method.

    Before and after

    Compare this calculation with a run you saved earlier on this tool (under “Saved runs”). The page shows what changed and by how much.

    A line through the data from your recorded table

    Pick two measured columns from the same table. The page plots them and draws the least-squares line, only across the range you measured.

    Robot log a CSV from the robot's SD card

    Load a CSV your robot saved. Pick the time column and up to three columns to plot, and type their units. Only those columns go on the page; the file stays on this device.

    Two versions' trials your data, compared

    Pick a column of recorded trials for each version, from this page or another saved page. The page shows both averages and a 95% range for the difference. The numbers are copied in when you pick them, so later changes to the other page don't change this one.

    Options compared your scores

    Score each option 1 to 5 on each criterion, and weight each criterion 1 to 5 by how much it matters. The page only multiplies and adds.

    Photos and sketches stay on this device

    Up to 4. Paste a screenshot with Ctrl+V, drop pictures here, or pick them. Photos are shrunk before they’re kept, and an unsaved page keeps them in its draft. Use Mark up to draw arrows, labels, dimensions and numbered callouts on a photo. Mark one photo Before and one After to print them side by side.

      Test plan written before testing

      Write this before you test: the question, what you expect with a number, and what result would make you drop the idea.

        Build steps our build

        One row per step, in order, so someone could rebuild from this page.

          Parts used our parts list

          Lengths in holes are also shown in inches between the end holes. Weights are only added up where you type them.

            Plan the cuts: packs every piece of one part (sizes in holes, or inches on the hole grid) onto whole sticks of the stock length you type.

            Ways it could fail our scores

            List the ways this could fail. Score how likely (1 to 5) and how bad (1 to 5); the page multiplies them and puts the biggest risks first.

              Designed against built our measurements

              What the CAD or the plan said, and what you measured on the robot. The tolerance is yours.

                Changes from the last version our changes

                What changed since the last version, why, and which result it was meant to move.

                  That page’s settings, results and first photo are copied in and set beside this page’s. The result each change should move is looked up on both pages.

                  Tasks our plan

                  What needs doing, who, and by when. Open tasks carry to the next meeting page until someone ticks them done.

                    The pages behind this idea our evidence

                    The pages in this notebook that show the idea being tried, measured or changed. A judge reading the claim can turn straight to them.

                      Time spent our hours

                      Who worked on this and for how long.

                        Session log what we did, as we did it

                        Notes taken during a session. The time comes from the clock when the note was taken; every word is yours.

                          Size limit does it fit?

                          Type the starting size limit from the current game manual, and the robot's size as designed or measured, in inches. The site doesn't store the limit, because it changes with the game.

                          What broke from your breakage log

                          The breakage log is on My notebook. Copy it onto this page as a table, as it stands now; later entries don't change this page.

                          CAD model which version this page is about

                          Paste a link to the model (Onshape, Fusion or anything else) and the name you use for this version. For Onshape, the page reads from the link whether it points at a saved version or a workspace that keeps changing. Nothing is fetched.

                          Your code
                          Comments notes for the team, not the page

                          A teammate or coach can leave a note here. Comments stay beside the page, travel with it in exports and links, and don't print unless you tick them under Include.

                            Sources you used besides this tool

                            Videos, other teams, manuals, people. The tool’s own sources are cited for you.

                              Sign-off
                              Include

                              Press a ? to see what an option is for, or read them all on How the notebook tools work.

                              What “The calculator’s figures” is for

                              The calculator’s own diagrams and charts, numbered as figures and drawn from your numbers. Judges look for pictures that explain a design.

                              What “How it was calculated” is for

                              The formulas and steps the calculator used, so a reader can check the arithmetic for themselves.

                              What “The calculator’s warnings” is for

                              Things the calculator flagged, such as a motor near stall. They’re quoted and credited to the calculator, so they never read as your conclusion.

                              What “The calculator’s notes” is for

                              The calculator’s plain-language notes on the result. Off at first, because they read like conclusions, and the conclusions on a page should be yours.

                              What “Lined space” is for

                              Ruled lines under any part you haven’t written yet, so a printed page can be finished by hand.

                              What “Writing space as” is for

                              The blank space for handwriting as ruled lines, a dot grid or quarter-inch squares. Dots and squares suit sketches and hand-drawn graphs.

                              What “A summary under recorded data” is for

                              The number of readings, the average, the spread, the lowest and the highest under each table you recorded, worked out from your numbers. It shows every run counted, not just the best one.

                              What “Words used” is for

                              A small box with the site’s one-line definitions of glossary terms the calculator used, for readers who don’t know them. It never looks at your own writing.

                              What “Robot at the time” is for

                              The Robot Profile as it was when the page was first saved, so weeks later you can tell which version of the robot a test was run on.

                              What “Long tables in full” is for

                              Long calculated tables printed complete on an extra page, instead of every few rows on the page itself.

                              What “Fit on one sheet” is for

                              Smaller type and shorter tables, aiming for one printed sheet. Use it when every entry in your notebook should be a single page.

                              What “Wider left margin” is for

                              A wider left edge, so the page can be hole-punched or bound without losing any words.

                              What “Larger type, for reading aloud” is for

                              Bigger print with more room between lines, for the team member who reads the page to a judge. It overrides Fit on one sheet.

                              What “Our rubric scores” is for

                              Your own scores against the rubric, on a sheet of their own, for checking a page before a judge does.

                              What “When this page was first saved” is for

                              The day the page was first saved, printed beside its date. It shows the notebook was kept while the work happened.

                              What “Teammates’ comments” is for

                              Prints the comments teammates left on this page at the end, marked as not part of the page. Off at first, because comments are notes for the team, not for judges.

                              What “Show every table and block” is for

                              Shows every table and block in the editor, not only the ones this type of page usually uses. It changes the editor, not the printed page.

                              Rubric check

                                This checks what is on the page, not how good it is. Clear, specific writing in your own words is what earns the top marks.

                                Preview, letter size

                                Write it now

                                Where this goes next

                                Explore further on the full map

                                Where the answers on this page can be used, and which tools could have given you the numbers it asks for.

                                Comes after

                                Gear Spacing Calculatorfills in your gear sizes here

                                You are here

                                Gear Ratio Calculator

                                Where your answer goes

                                Drivetrain Speed Calculatorturn that ratio into an actual top speed in ft/sbrings your gear sizes with itTorque & Stall Checkcheck the motors can survive that ratio under loadbrings your gear sizes with itGear Spacing Calculatorcheck the pair lands on the hole grid before you build itbrings your gear sizes with itPushing Force & Traction Limitfind out how hard that ratio lets you push before the wheels slipbrings your gear sizes with it

                                a number carries across the next question it raises

                                Keyboard shortcuts

                                Anywhere

                                Ctrl K or /
                                Search
                                T
                                Switch color theme
                                B
                                Bigger text, for a projector
                                F
                                Readable font, on or off
                                ?
                                This list

                                On a tool

                                S
                                Star or unstar it
                                C
                                Copy the results
                                L
                                Copy a link to these exact numbers
                                P
                                Print or save as PDF

                                Letter keys do nothing while you're typing in a box.