Free belt calculator · No sign-up · Exact tangent geometry

Pulley & Belt Length Calculator

Calculate belt length for any two-pulley drive: open or crossed, flat, V-belt or timing. Per-field mm/in mixing, V-belt pitch–outside–inside conversion, timing belt tooth counts, RPM ratio and belt speed — plus the nearest standard belt you can actually buy. Left side: your inputs. Right side: the numbers.

⚙️Inputs

unit · RPM optional
unit · RPM optional
Belt Length (L) = 851.11 mmØ 101.60 mmØ 50.80 mmC = 304.80 mm

📏Results

Output units

Belt length · open · pitch line

C = 304.80 mm

851.11mm

Outside

851.11 mm

Pitch

851.11 mm

Inside

851.11 mm

Speed & ratio

Ratio

2.000 : 1

driver : driven

Driver RPM

1750

Driven RPM

875

Belt speed

4.65

ms

Leave either RPM box empty and it is derived from the pulley diameters. Enter both and they are cross-checked against the ratio.

Geometry check

PD₁

50.80 mm

PD₂

101.60 mm

Pulley gap

228.60 mm

edge to edge

Wrap small

170.4°

Wrap large

189.6°

Pulley gap / span

75%

of center distance

Engineering accuracy: Formulas based on RMA (Rubber Manufacturers Association) and ISO mechanical standards. Designed for engineers and DIY mechanics.

⚡Quick answers people search for most

Common belt-drive setups computed with the same engine that powers the tool above — click through to the calculator and swap in your own numbers.

⚙️

2 in + 4 in pulleys · 12 in centers · open

33.5 in

The classic shop setup: a 2:1 reduction on 12-inch centers needs roughly a 33–34 inch belt.

✕

Same drive, crossed belt (8-shape)

34.2 in

Crossing adds about 2–3 inches versus an open belt on the same pulleys and reverses the driven rotation.

▼

A-section on OD 2.0 / 4.45 · 12 in

33.6 in pitch

V-belt thickness lifts the working circumference above the bare pulley geometry — pitch-line math catches it.

🦷

GT2 · 20T + 40T · 60 mm centers

90 teeth

3D printers and CNC: enter pulley teeth directly and get the belt tooth count you actually order.

🌀

1750 RPM on a 2 in pulley

≈ 4.7 m/s

Belt speed = π × pitch diameter × RPM. A 2 in pulley at 1750 RPM runs ~918 ft/min — well inside V-belt limits.

📐

Wrap angle rule of thumb

≥ 120°

Below 120° of wrap on the small pulley, traction collapses. Raise the center distance, cut the ratio, or add an idler.

🛒

Calculated 42.3 in A-belt → buy

A42

Belts come in whole-inch inside lengths. The tool maps your exact figure to the nearest stock designation with the delta shown.

🧮Pulley belt length calculator formulas, exactly as computed

No black boxes — the calculator runs these equations on every keystroke. All lengths are measured at the pitch line; the V-belt length calculation formula layers section-specific thickness offsets on top of the raw geometry.

Open belt (parallel rotation)

L = 2C·cos φ + r₁(π − 2φ) + r₂(π + 2φ)
φ = arcsin((r₂ − r₁) / C)

The engineering shortcut L ≈ 2C + (π/2)(D₁ + D₂) + (D₂ − D₁)²/(4C) is the small-angle expansion of the same result — identical on everyday drives, but the exact form stays accurate on tight centers and big ratios where the shortcut can miss by several millimeters.

Crossed belt (reversed rotation)

L = 2C·cos φ + (r₁ + r₂)(π + 2φ)
φ = arcsin((r₁ + r₂) / C)

Both pulleys gain wrap (180° + 2φ each) and the difference term (D₂ − D₁)² becomes a sum term (D₂ + D₁)² — crossed belts are always longer than open belts on the same pulleys. Both strands cross at r₁/(r₁ + r₂) × C from the driver's center, which the calculator reports for clearance checks.

Solving backwards is closed-form, not guesswork. Given a belt length instead of a center distance, the quadratic 2C² − (L − A)C + B = 0 (with A = (π/2)(D₁ + D₂), B = (D₂ − D₁)²/4) is solved — then refined against the exact tangent formula — so "I own a 40-inch belt, where do the shafts go?" returns an exact answer. The same solver positions the center distance that makes a stocked timing-belt tooth count fit your pulleys.

▼V-belt length calculator: cross-section data & length conversions

Datum dimensions per section (RMA / ISO), and what a 1,000 mm pitch-line belt measures outside and inside — the offsets the calculator applies for you.

SectionFamilyTop widthThicknessOD − PD / pulleyOutside − pitchPitch − insideSold as (≈1000 mm)
Aclassical13 mm8 mm5.6 mm+17.6 mm−32.7 mmA38
Bclassical17 mm11 mm7.4 mm+23.2 mm−45.9 mmB38
Cclassical22 mm14 mm9.4 mm+29.5 mm−58.4 mmC37
Dclassical32 mm19 mm12.6 mm+39.6 mm−79.8 mmD36
3Vnarrow9.5 mm8 mm5.6 mm+17.6 mm−32.7 mm3V390
5Vnarrow16 mm13.5 mm9.0 mm+28.3 mm−56.5 mm5V500
8Vnarrow25.5 mm17.5 mm11.8 mm+37.1 mm−72.9 mm8V800
SPZmetric9.7 mm8 mm5.0 mm+15.7 mm−34.6 mmSPZ1000
SPAmetric12.7 mm10 mm6.6 mm+20.7 mm−42.1 mmSPA1000
SPBmetric16.3 mm13 mm8.6 mm+27.0 mm−54.7 mmSPB1000
SPCmetric22.5 mm18 mm12.0 mm+37.7 mm−75.4 mmSPC2000

Buying rules by family: classical A/B/C/D belts are sold by inside length in whole inches (A45 = 45 in inside); narrow 3V/5V/8V by pitch length in inches ×10 (3V500 = 50.0 in pitch); metric SPZ/SPA/SPB/SPC by ISO datum length in mm (SPZ 1250). The calculator's part-number matcher maps your exact result to the nearest stock designation in the right system, with the delta printed.

🦷Timing belt calculator: pitch reference

Tooth spacing for the profiles this timing pulley belt length calculator supports — enter pulley teeth plus one of these pitches and get the belt tooth count to order.

ProfilePitch (mm)Pitch (in)PD of a 20T pulleyTypical use
MXL2.0320.080012.94 mmSmall hobby drives, printers, encoders
XL5.0800.200032.34 mmSmall hobby drives, printers, encoders
L9.5250.375060.64 mmLight industrial, conveyors, older CNC
H12.7000.500080.85 mmLight industrial, conveyors, older CNC
GT22.0000.078712.73 mm3D printers, CNC, robotics (FRC) — zero-backlash
GT33.0000.118119.10 mm3D printers, CNC, robotics (FRC) — zero-backlash
GT55.0000.196931.83 mm3D printers, CNC, robotics (FRC) — zero-backlash
3M3.0000.118119.10 mmHTD power transfer (3 mm)
5M5.0000.196931.83 mmHTD power transfer (5 mm)
8M8.0000.315050.93 mmHTD power transfer (8 mm)
14M14.0000.551289.13 mmHTD power transfer (14 mm)

Worked timing example: 20T driver + 40T driven (GT2, 2 mm pitch) on 60 mm centers → pulley PDs of 12.73 mm and 25.46 mm, an exact requirement of 90.3 teeth, and a stocked belt of 90 teeth (180 mm) that fits at an adjusted center distance of 59.7 mm.

📝How to use the belt length calculator (metric & inch)

Eight steps from two shafts and a tape measure to the belt designation you can order — the same workflow a drive engineer runs, minus the handbook.

1

Pick the belt arrangement

Open belt for standard parallel rotation, crossed belt when the driven shaft must spin the opposite way. The formula switches automatically — crossed belts wrap both pulleys more, so the belt is longer.

2

Pick the belt type

Flat/round uses pure pulley geometry. V-belt adds the cross-section's thickness so you get pitch, outside and inside lengths. Timing mode swaps diameters for tooth counts and outputs the belt tooth count you need to order.

3

Enter both pulley diameters — in any units

Each field carries its own unit dropdown (mm / cm / m / in / ft). Enter the driver in inches and the driven pulley in millimeters if that's how your drawings are dimensioned — everything is unified internally, nothing needs pre-converting.

4

Choose OD or pitch diameter (V-belts)

Calipers give you outside diameter; catalogs give pitch diameter. Select the basis you measured and the tool converts through the cross-section's pitch-line offset automatically.

5

Enter the center distance — or the belt you already own

Most people know the shaft-to-shaft distance. Working backwards from a belt in hand? Flip to 'I know the belt length' and the tool solves the required center distance instead.

6

Optionally add one RPM

Type the motor RPM and the driven speed, the exact speed ratio and the belt speed appear instantly — one extra field, no separate calculator. Enter both RPMs and they are cross-checked against the pulley ratio to expose slipping or mis-measurement.

7

Read the outputs in the units you think in

The output unit dropdown switches every length result live — enter in inches, read the belt length in millimeters, check belt speed in ft/min. Warnings flag small wrap angles, extreme ratios and overspeed before they cost you a belt.

8

Buy the real belt, not the decimal

V-belt results include the nearest stock designation (A42, 3V500, SPZ 1250…) with the exact delta versus your calculated length. Timing results give the tooth count to order and the adjusted center distance it implies.

🧪Worked example: A-section V-belt, OD inputs, 1750 RPM motor

Every number below comes from the same transparent math the calculator runs — a 2.00 in driver and a 4.45 in driven pulley measured with calipers, on 12 in centers.

The math, step by step

  1. OD → pitch diameter: the A-section pitch line sits 2.8 mm below the belt top, so PD = OD − 5.6 mm. Driver 45.2 mm, driven 107.4 mm.
  2. Wrap angle: φ = arcsin((r₂ − r₁)/C) = arcsin(0.1021) → wrap on the small pulley 168.3°, on the large one 191.7° — both above the 120° floor. ✓
  3. Exact open-belt length: L = 2C·cos φ + r₁(π − 2φ) + r₂(π + 2φ) = 33.56 in at the pitch line.
  4. Thickness offsets: outside = pitch + 17.6 mm, inside = pitch − 32.7 mm → 34.26 in outside / 32.28 in inside.
  5. Speed: ratio D₂/D₁ = 2.377 : 1 → 1750 RPM in gives 736 RPM out; belt speed 4.14 m/s — inside the 30 m/s V-belt ceiling. ✓
  6. Stock match: 32.28 in inside length rounds to A32 — the purchased belt's pitch length differs by 0.28 in from the calculated one.

Calculator output for this example

Pitch length

33.56 in

852.5 mm at the cord line

Inside / Outside

32.28 / 34.26 in

buy by inside length

Center distance solved

12.000 in

as entered

Ratio & driven RPM

2.377 : 1 · 736 RPM

1750 RPM motor

Belt speed

4.14 m/s

≈ 815 ft/min

Nearest stock belt

A32

0.28 in vs calculated

❓Frequently Asked Questions

The belt-drive questions we get most often — answered with the same formulas the calculator runs.

How do I calculate belt length for two pulleys?

+
For an open belt, the standard engineering formula is L = 2C + (π/2)(D₁ + D₂) + (D₂ − D₁)²/(4C), where C is the center distance and D₁, D₂ the pitch diameters. This calculator uses the exact tangent-line version of that formula — L = 2C·cos φ + r₁(π − 2φ) + r₂(π + 2φ) with φ = arcsin((r₂ − r₁)/C) — which stays accurate for large ratios and short centers where the shortcut formula drifts. Both reduce to the same numbers on everyday drives: a 2-inch and a 4-inch pulley on 12-inch centers need about a 33.6-inch belt.

Does a crossed belt change the belt length?

+
Yes — meaningfully. In a crossed (figure-8) drive both pulleys carry extra wrap, and the difference term flips sign: L = 2C + (π/2)(D₁ + D₂) + (D₂ + D₁)²/(4C). The same 2-inch/4-inch drive on 12-inch centers that needs ~33.6 inches open requires roughly 36 inches crossed — about 2.4 inches more. Crossed belts also reverse the driven pulley's rotation and rub where the strands cross, so they suit light-duty drives; the calculator reports the crossing-point distance along the shaft line so you can check clearance.

What is the difference between pitch length, outside length and inside length?

+
A V-belt is a wedge of rubber and cords with real thickness, so 'the belt length' depends on where you measure. Pitch length is measured at the cord line (the neutral axis that doesn't stretch) — it's the number catalogs are built around. Outside length runs longer than pitch by roughly 2π times the distance from the top cover to the cords (about 0.65 in for an A-section); inside length runs shorter by about 2π times the remaining thickness (about 1.3 in for A). Buying rules follow the section: classical A/B/C/D belts are sold by inside length, narrow 3V/5V/8V by pitch length, metric SPZ–SPC by ISO datum length. The calculator outputs all three so you can match whichever label the seller prints.

Should I enter outside diameter (OD) or pitch diameter (PD)?

+
Whichever you actually have. Calipers on a pulley give you OD; a catalog or a stamped marking usually gives PD. For a V-belt pulley the two differ by twice the pitch-line offset of the belt section (e.g., an A-section pulley's PD is about 5.6 mm smaller than its OD). Select the measurement basis in the calculator and the conversion happens inside the math — guessing wrong shifts the belt length by π times that error, which is one of the most common reasons a purchased belt 'doesn't fit'.

Can I mix units — inches for pulleys and millimeters for center distance?

+
That's the default workflow here, not a workaround. Every input field (D₁, D₂, center distance, belt length) carries its own independent unit dropdown — mm, cm, m, in or ft — and the engine converts everything to a common base before computing. Outputs have their own switchable unit too, so you can dimension a metric drawing, order belts from a US supplier in inches, and read every intermediate value in whichever system you think in, without touching a conversion chart.

How do I size a timing belt by teeth instead of millimeters?

+
Timing belts are sold by tooth count, so this tool lets you enter pulley teeth (T₁, T₂) plus the belt pitch (GT2 2 mm, GT3, 5M, MXL, XL, L, H…) directly. Each pulley's pitch diameter is derived as d = p × T / π, the exact belt length is computed, then divided by the pitch to give the required tooth count — and rounded to the nearest tooth count that is actually stocked (even counts for metric pitches). Because a stocked belt rarely matches the exact count, the calculator also solves the adjusted center distance that makes the real belt fit, which tells you how much slot or tensioner travel your mounting needs.

Why is the belt I calculated not the belt I can buy?

+
Manufacturers make belts in standard steps — whole inches of inside length for classical A/B/C/D, inch-based pitch designations for 3V/5V/8V, and an ISO length series (530, 560, 600, 630… mm) for SPZ–SPC. A calculated 42.3-inch A-belt doesn't exist; the nearest stock belts are A42 and A43. The calculator maps every V-belt result to the closest stock designation and prints the exact delta (e.g. −0.2 in). A belt slightly long tensions fine; a belt slightly short must be forced over the pulleys, so treat small negative deltas with suspicion.

What wrap angle do pulleys need?

+
Traction lives in the contact arc. The rule of thumb: at least 120° of wrap on the smaller pulley (and never below 90°). Wrap on the small pulley is 180° − 2φ where φ depends on the diameter difference and center distance, so big ratios on tight centers starve the small pulley of grip. The calculator reports both wrap angles live and warns below 120° — the fixes, in order of cost, are a longer center distance, a smaller ratio, or an idler/tensioner that pushes the belt onto the small pulley.

How fast is my belt moving, and does it matter?

+
Belt speed = π × pitch diameter × RPM. It matters because V-belts are limited to roughly 30 m/s (about 5,900 ft/min): beyond that, centrifugal force lifts the belt out of the sheave groove and capacity collapses. A 2-inch pulley at a typical 1750 RPM motor runs ~4.7 m/s — comfortably safe — while the same belt on an 8,000 RPM spindle at 75 mm is pushing 9.4 m/s, still fine. The calculator reports belt speed in m/s, ft/min, km/h or mph and warns when you cross the practical ceiling. For timing belts, speed is less limiting than tooth mesh frequency — above ~10,000 RPM check the manufacturer's curve.

What ratio can one belt stage handle?

+
Practical single-stage V-belt ratios top out around 8:1 (and bottom at 1:8) because the small pulley's wrap angle and the arc of approach both deteriorate as the diameters diverge. Timing belts are similar in practice, though small-pitch GT profiles handle higher ratios on short centers better than classical sections. If you need more, stage the reduction through a jackshaft — two 4:1 stages give 16:1 with healthy wrap everywhere. The calculator flags ratios beyond the practical band automatically.

How tight should a belt be tensioned?

+
Tension is set by belt deflection, not feel: press at mid-span with roughly the recommended force and the belt should deflect about 1.6 mm per 100 mm of span (1/64 inch per inch) for V-belts, per typical manufacturer tables. Too loose and it squeals and slips under load pulses (glazing the sidewalls); too tight and the bearings pay for it — a common failure on small motors with short shafts. After fitting a 'slightly long' matched belt, plan on a tensioner or slotted mount to take up the difference the part-number matcher reports.

How accurate is this belt calculator?

+
The geometry is exact: tangent-line belt length, wrap angles, crossing point and the closed-form center-distance solution are computed from your numbers without the small-angle shortcuts that drift on tight centers. The V-belt thickness offsets use published datum dimensions for each section (A/B/C/D, 3V/5V/8V, SPZ/SPA/SPB/SPC) and are accurate to about a millimeter; real manufacturing tolerances add ±2–3 mm anyway. Timing-belt tooth availability is rounded to commonly stocked counts, so always confirm the exact designation with your supplier before ordering.

Is there a V-belt length calculator app I can use offline?

+
Yes — this page is a free, install-free V-belt length calculator app that runs in any phone, tablet or desktop browser and keeps working offline once loaded. The same tool doubles as a metric belt length calculator (mm, cm, m) and an inch-based one (in, ft), with every input field carrying its own unit selector. Under the hood it applies the V-belt length calculation formula for A/B/C/D, 3V/5V/8V and SPZ–SPC sections with pitch, outside and inside lengths, plus a dedicated timing pulley belt length calculator mode that converts pulley teeth and pitch into the exact tooth count to order.