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Chain Length Calculator

How many links a chain run needs, and more usefully, what center distance a whole number of links actually gives you.

Inputs

A sprocket only fits the chain it was made for, and the two sizes are not interchangeable. Picking the type sets both the pitch and the sprockets you can choose.

in

Distance between the two shafts.

in

Read the warning below before trusting this default. To measure your own: lay out 20 links, measure end to end, divide by 20.

Results

Links needed

—

Rounded up to a whole link.

Exact figure

—links

Nearest even link count

—

Even avoids a weak offset link.

Center distance at that whole link count

—in

Difference from what you asked for

—in

Chain length

—in

Pull the sprockets apart

Pull the sprockets apart
6 in

Your two sprockets drawn to scale at their pitch circles, with the chain wrapped around them. Slide them apart and the chain needs more links, but it can only come in whole ones. The dashed sprocket is where the second shaft has to sit for the whole number of links the page rounds to, which is why the distance you get is rarely the distance you asked for.

How this is calculated

Chain length is not just twice the center distance. The chain also wraps around both sprockets, and when the two sprockets differ in size the run between them sits at a slight angle, which adds a little more:

links = 2C/p + (N₁ + N₂)/2 + p·((N₂ − N₁)/2π)² / C C = center distance p = chain pitch N₁ = teeth on first sprocket N₂ = teeth on second

The first term is the two straight runs, the second is the wrap around both sprockets, and the third is the small correction for unequal sprockets. That third term vanishes when both sprockets are the same size.

The part that actually matters

Chain comes in whole links. You almost never get the center distance you asked for. You get the one the nearest whole link count gives you. So this calculator runs the formula backwards too:

C = (p/8) · [ 2L − N₁ − N₂ + √( (2L − N₁ − N₂)² − (8/π²)(N₂ − N₁)² ) ]

Design your mounting holes around that number, not the one you first thought of. A chain cut to the right length and mounted at the wrong distance is either too slack to stay on or too tight to turn.

Odd links

An odd number of links needs an offset link to close the loop, and an offset link is the weakest part of the chain. Where you have the freedom, take the even count. Where you do not, tension it properly and expect it to be the first thing that fails.

Leave room to tension

Chain stretches with use. A run mounted at exactly the calculated distance with no adjustment will go slack and start skipping teeth. Either mount one shaft in a slot, or plan on an idler sprocket taking up the slack.

Sources & assumptions

Sprocket tooth counts are the confirmed contents of the VEX High Strength Sprocket & Chain Kit (276-2252). Sprocket pitch diameter is computed as pitch ÷ sin(180°/teeth), the standard roller chain geometry, rather than from the kit's approximate outer diameters.

The chain pitch default is derived from that kit listing (140 links, 54 inches) and is the weakest number on this page. Every result scales directly with it. Measure your own chain and override it.

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.

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    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.

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

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

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    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.

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    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.

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    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.

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    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

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                  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.

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                          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.

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

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                              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

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                              What “Long tables in full” is for

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                              What “Fit on one sheet” is for

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                              What “Wider left margin” is for

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                              What “Larger type, for reading aloud” is for

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                              What “Teammates’ comments” is for

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                                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.

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                                Where this goes next

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

                                Comes after

                                Chain & Sprocket Ratio Calculatorfills in your sprocket sizes hereGear Spacing Calculatorfills in your center distance here

                                You are here

                                Chain Length Calculator

                                Where your answer goes

                                Chain & Sprocket Ratio Calculatorsee what speed and torque that sprocket pair gives youbrings your sprocket sizes with itSpacer Stack Calculatorline the sprockets up exactly so the chain stays on

                                a number carries across the next question it raises

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