Belt calculator tools & features
One page hosts the whole toolchain — the flagship belt length calculator plus every feature folded inside it. This directory organizes those features by the questions they answer: getting the geometry right, mixing the units your shop actually speaks, converting a V-belt section into a purchasable part number, and checking speed before it checks you. All free, all in-browser, all storing nothing on our servers.
The Belt Length Calculator
Left side: your drive — belt type, pulley diameters (or tooth counts), center distance, optional RPM. Right side: the numbers — belt length in three conventions, wrap angles, speed ratio, belt line speed, and the nearest standard belt or tooth count you can actually buy, with every engineering warning attached.
It is deliberately opinionated about transparency. There is no hidden rounding anywhere in the output: the exact tangent geometry, the section thickness offsets, the stock-match delta and each warning are separate, named figures. Switch the output unit and watch every result re-render; flip to 'I know the belt length' and the engine solves the center distance instead.
You get, per run
- →Belt pitch / outside / inside length
- →Pitch diameters from OD or PD input
- →Wrap angle on both pulleys
- →Speed ratio & driven RPM
- →Belt line speed (m/s & ft/min)
- →SVG drive diagram, to scale
- →Stock designation + exact delta
- →Timing teeth count & adjusted centers
⚙️Core length engine
The heart of the site: exact tangent-line belt length for open and crossed two-pulley drives, plus the reverse solve that turns a belt you own into a center distance.
Belt length looks like a one-line formula, and that is exactly why so many tools get it subtly wrong. The honest version is tangent-line geometry: the belt runs straight between the pulleys along lines that touch both circles, wraps each pulley over an arc that depends on the diameter difference, and the wrap arcs grow as the center distance shrinks. This engine computes that exact figure — L = 2C·cos φ + r₁(π − 2φ) + r₂(π + 2φ) with φ = arcsin((r₂ − r₁)/C) — and stays accurate on tight centers and large ratios where the textbook shortcut L ≈ 2C + (π/2)(D₁ + D₂) + (D₂ − D₁)²/(4C) drifts by millimeters.
Crossed drives get their own closed-form solution, not a fudge factor. In a figure-8 arrangement the difference term becomes a sum, both pulleys gain wrap (180° + 2φ each), and the belt is always longer than an open belt on the same pulleys — typically 2–3 inches on a small shop drive. The engine also reports the crossing-point distance along the shaft line, because a crossed belt that rubs a machine member on the way across is a belt that will not survive its first week.
The reverse solve answers the question people actually bring to the workbench: 'I have a belt in hand — where do the shafts go?' Given the belt length instead of the center distance, the engine solves for C against the exact tangent formula by bisection until it converges, and tells you plainly when the belt is physically too short to span the pulleys at all. Every run also renders a live, to-scale SVG of the drive — pulleys, tangent lines and wrap arcs drawn from your own numbers — so a geometry mistake is visible long before it reaches the parts counter.
Open-belt exact length
Tangent-line pitch length computed from r₁, r₂ and C without small-angle shortcuts — accurate on tight centers and big ratios where the shortcut formula misses.
Crossed-belt (figure-8) mode
The crossed formula's own closed form, rotation-reversal noted, plus the crossing-point distance from the driver's center for clearance checks.
Reverse solve: belt → center distance
Enter a belt you already own and the engine bisects against the exact formula for the center distance that fits it — or proves the belt is too short.
Live SVG drive diagram
A to-scale rendering of your pulleys, belt and wrap arcs that redraws on every keystroke — mistakes you can see are mistakes you can fix.
📐Per-field unit mixing
Every input field carries its own mm / cm / m / in / ft dropdown, and the output unit switches independently — because real drawings and real tape measures never agree.
Most calculators force one unit system per session, which quietly assumes your workshop is fully metric or fully imperial. Reality is messier: the lathe is dimensioned in inches, the replacement pulley box is labeled in millimeters, the shaft-to-shaft distance is whatever your tape measure said in feet and the belt catalog speaks inside-length inches. This tool treats the unit as a property of each field, not of the session — driver diameter in inches, driven diameter in millimeters, center distance in centimeters, all in the same calculation, with no pre-conversion and no conversion chart on the desk.
The engine's discipline comes from a single internal base: every value is converted to millimeters the moment it is entered, all math runs in that base, and results are formatted back out in whichever unit you select. Output switching is live — enter the drive in inches and read the belt length in millimeters, flip the belt speed between m/s and ft/min, and the underlying numbers never round-trip through your manual arithmetic. That design kills the most common silent failure in belt work: a converted value transcribed once, wrongly, and trusted ever after.
Mixed-unit entry also means mixed-source verification is cheap. Measure the old pulley with calipers in millimeters, cross-check the marking stamped in inches, and let the tool show both — if the two disagree by more than the section thickness explains, you have found a mislabeled part before it found you.
Independent unit per field
D₁, D₂, center distance and belt length each carry their own mm / cm / m / in / ft dropdown — inches and millimeters can live in the same calculation.
Switchable output units
One dropdown re-renders every length result live — enter in inches, read belt length in millimeters, check belt speed in ft/min or mph.
One internal base (mm)
Values convert to millimeters on entry; all math runs in that base and formats back out — no manual conversion step anywhere in the workflow.
Cross-source verification
Enter the same pulley from calipers and from a stamped marking in different units and spot a mislabeled part in seconds.
▼V-belt intelligence
Eleven cross-sections with real datum dimensions drive the thickness math: OD ↔ pitch diameter conversion, three length conventions, and stock designation matching with the delta shown.
A V-belt is a wedge of rubber and cords with real thickness, and ignoring that thickness is the single most common way belt calculators produce a belt that doesn't fit. The registry here covers the classical sections (A, B, C, D), the narrow sections (3V, 5V, 8V) and the metric SP sections (SPZ, SPA, SPB, SPC) — each with its published top width, height, and pitch-line offset. Select a section and the whole engine changes behavior: measured diameters convert from outside to pitch through the section's own offset, and the length result splits into pitch, outside and inside conventions.
The three conventions exist because three different labels exist. Pitch length runs at the cord line — the neutral axis that does not stretch — and is what catalogs engineer around. Outside length runs longer by 2π times the top-cover offset; inside length runs shorter by 2π times the remaining thickness. Buying rules follow the section family: classical A/B/C/D belts are sold by inside length in whole inches (A42 means 42 inches inside), narrow 3V/5V/8V by pitch length in inches × 10 (3V500 = 50.0 inches pitch), and metric SP belts by the ISO 4184 datum series (SPZ1250 = 1250 mm datum).
The matcher closes the gap between a calculated decimal and a purchasable box. Every V-belt result maps to the nearest stock designation — A42, 3V500, SPZ 1250 — and prints the exact delta between the purchased belt's pitch length and your calculated pitch length. A belt slightly long tensions fine; a belt slightly short must be forced over the pulleys, so a small negative delta deserves suspicion, and the delta display is how you catch it before the belt doesn't.
11 cross-section registry
Classical A/B/C/D, narrow 3V/5V/8V and metric SPZ/SPA/SPB/SPC — each with top width, height and pitch-line offset applied through the math.
OD ↔ pitch diameter conversion
Calipers give outside diameter; catalogs give pitch diameter. Pick the basis you measured and the section's offset converts inside the calculation.
Pitch / outside / inside lengths
Every result reports all three conventions so you can match whichever label the seller prints — cord line, top of belt, or inner face.
Stock designation matcher
Calculated 42.3 in becomes A42; 1276 mm becomes SPZ 1250 — with the exact purchased-vs-calculated delta printed next to the part number.
⚡Speed & timing
Speed ratio, driven RPM and belt line speed in one pass — plus a timing mode that works in tooth counts and solves the adjusted center distance for the belt you can actually buy.
Belt drives are speed machines before they are length problems, and the speed math costs nothing extra here. Enter one RPM (usually the motor plate) and the exact ratio n₁/n₂ falls out of the pulley diameters, driven RPM with it, and belt line speed — π × pitch diameter × RPM — comes reported in m/s, ft/min, km/h or mph. Enter both RPMs and they are cross-checked against the pulley ratio: when the pair implies a different ratio than the geometry, something is slipping or a pulley is mis-measured, and the tool says which side it believes.
The warnings attached to that math are the difference between a number and a design review. Belt speed above ~30 m/s lifts a V-belt out of its sheave groove and collapses capacity; a ratio beyond the practical 8:1 band starves the small pulley of wrap; wrap angle below 120° on the small pulley breaks traction under load pulses. Each condition is flagged live, with the standard fixes named — longer center distance, smaller ratio, or an idler — rather than left for you to discover in a handbook.
Timing mode rethinks the inputs entirely, because timing belts are bought by teeth. Pick a pitch (MXL, XL, L, H, GT2, GT3, GT5, HTD 3M/5M/8M/14M), enter pulley teeth instead of diameters, and the engine derives each pitch diameter as d = p × T / π, computes the exact belt length, divides by the pitch for the required tooth count, and rounds to the nearest commonly stocked count. Because the stocked belt rarely matches the exact figure, the adjusted center distance that makes the real belt fit is solved too — which is the number your mounting slot or tensioner actually needs to accommodate.
Speed ratio & driven RPM
One motor RPM in, exact ratio and driven speed out — and an entered RPM pair gets cross-checked against the pulley geometry to expose slip.
Belt line speed
π × pitch diameter × RPM reported in m/s, ft/min, km/h or mph, with the ~30 m/s V-belt ceiling flagged when you cross it.
Timing pitch presets (11)
MXL, XL, L, H, GT2, GT3, GT5 and HTD 3M–14M — pick the pitch, enter tooth counts, and pitch diameters derive as d = p × T / π.
Teeth count & adjusted centers
Exact required teeth, the nearest stocked count, and the center distance that makes the stocked belt fit — the number your slot or tensioner needs.
A run through the toolchain: re-belt a lathe spindle
The tools are designed as one pass, not a quiz — six decision points from a dead machine to a part number, in about two minutes. This walkthrough follows a classic shop scenario: an A-section V-belt on a motor and spindle, measured in mixed units.
Measure what the machine actually has
Calipers across both sheaves read 2.00 in and 4.45 in outside diameter. V-belt mode is selected and 'I measured OD' is checked, so the A-section's pitch-line offset converts both readings to working pitch diameters inside the engine — no hand subtraction of twice the datum offset.
Pick the section from the belt in hand
The old belt's top width measures 13 mm: that's a classical A (13 × 8 mm). Selecting 'A' loads the section's height and pitch-line offset into every subsequent number — the same registry that powers the homepage's section table.
Enter the center distance in the units you measured it
Shaft-to-shaft distance reads 12 inches on the tape. Typed into the center-distance field with its unit dropdown left on 'in'. The motor pulley could just as well have been entered in millimeters — the engine converts each field to its internal base independently.
Read the geometry, then the warnings
The result: about a 42-inch-class belt with both wrap angles shown — comfortably above the 120° rule — and a belt speed near 4.7 m/s at the 1750 RPM motor plate, far below the 30 m/s ceiling. Nothing to fix, everything on record.
Take the part number, not the decimal
The calculated pitch length is not purchasable, so the matcher renders the verdict: A42, with the exact delta versus the calculated length printed beside it. Classical belts are sold by inside length in whole inches, and the delta display shows precisely how far off the nearest stock belt runs.
Order, fit, tension, done
The URL now encodes the entire configuration — bookmark it into the machine's maintenance log or text it to the supplier. A slightly long belt tensions fine on the lathe's slotted motor mount; had the delta run negative, the walkthrough would end at the counter asking for the next size up instead.
Which tool answers which question
The six questions every belt buyer eventually asks, and the feature built to answer each one.
| The question | The tool | How it answers |
|---|---|---|
| How long is the belt for these two pulleys? | Core length engine (open or crossed) | Exact tangent-line geometry from r₁, r₂ and C, with the SVG diagram exposing wrap arcs and tangency at a glance. |
| I own a belt — where do the shafts go? | Reverse solve: belt → center distance | Bisection against the exact formula returns the center distance that fits the belt, or proves it is physically too short. |
| My drawing is metric and my tape is imperial | Per-field unit mixing | Each field carries its own mm/cm/m/in/ft dropdown; everything converts to a common internal base with no pre-conversion. |
| Which V-belt does this caliper reading mean? | OD ↔ PD conversion + section registry | Eleven sections with datum offsets convert outside diameter to pitch diameter and split results into pitch/outside/inside lengths. |
| What belt do I actually order? | Stock designation matcher | A42 / 3V500 / SPZ 1250 with the exact purchased-vs-calculated delta — the number the parts counter needs, not the decimal. |
| Will this drive run without slipping or flying apart? | Speed & warning pass | Ratio, driven RPM, belt speed and wrap angles checked live against the 8:1, 120° and 30 m/s practical limits. |
Tool questions, answered
Is this a different calculator from the one on the homepage?+
It's the same engine, organized. The homepage runs the full calculator with its formula cards, section data tables and worked example around it; this page is the directory that explains what each part of the tool does and which problem it solves. Both lead to the same result — this page just maps the terrain first.
Can I really mix units between fields?+
Yes — that's the default workflow here, not a workaround. Each of the four length inputs (both pulley diameters, center distance, belt length) carries an independent mm / cm / m / in / ft dropdown, and the engine converts every value to millimeters internally before computing. Outputs switch independently, so nothing ever needs pre-converting on paper.
What exactly does the stock matcher give me?+
A purchasable designation plus honesty about the rounding. Classical belts come back as A/B/C/D + whole inches of inside length, narrow belts as 3V/5V/8V + pitch length × 10, metric belts as SPZ/SPA/SPB/SPC + ISO datum length — each with the delta in pitch length versus your calculated figure. A slightly long delta tensions fine; a slightly short one deserves suspicion.
Do I need to know my belt's cross-section to use the tool?+
For flat-belt and timing work, no — timing mode asks for a pitch and tooth counts instead. For V-belt work the section drives the thickness math, but measuring the old belt's top width (13 mm ≈ A, 17 mm ≈ B, 22 mm ≈ C) or its width class (9.5 mm ≈ 3V, 16 mm ≈ 5V, 25.5 mm ≈ 8V) takes ten seconds with calipers and makes every downstream number exact.
Why does the tool warn about belt speed?+
Because the failure is invisible until it happens. Above roughly 30 m/s, centrifugal force lifts a V-belt out of its sheave groove, contact pressure collapses, and capacity with it — the belt often still looks fine on the shelf. The warning names the measured speed so you can balance pulleys, reduce RPM, or check the belt's rating before the drive teaches you the same lesson.
Does anything here cost money or require an account?+
No. Every tool on this page is free, runs entirely in your browser, and requires no sign-up. Nothing is stored on our servers, and any configuration you want to keep encodes into the page URL — bookmark it or send it, and it reopens identically.
Want the drive knowledge behind the numbers? The belt drive & maintenance guides cover belt sections, measurement, drive design and installation — or go straight to the calculator.
Two pulleys and a tape measure is all it takes to start
Enter your diameters and center distance — or a belt you already own — and watch the toolchain turn your drive into a result you can actually order against.
⚙️ Run the calculator