The calculator runs the DIN 7753-2 drive calculation for an open two-pulley drive with narrow V-belts: from power, speeds, belt section and pulley diameters follow the speed ratio, the provisional belt length, the next standard length per DIN 7753-1/ISO 4184, the centre distance recalculated from it with take-up allowances, the wrap angle and the correction factors c1, c2 and c3 – and from these the required number of belts z = P·c2/(PN·c1·c3). The rated power per belt PN is taken from the power tables of the standard or the manufacturer's catalogue.
Two-pulley drive with narrow V-belts to DIN 7753-1 and pulleys to DIN 2211/ISO 4183; PN from table or catalogue; belt speed and flex frequency are checked against reference limits.
Define drive, belt section and operating conditions. The defaults are the worked example of DIN 7753-2 (lathe, 22 kW).
The calculator determines, for an open two-pulley drive with narrow V-belts, the speed ratio, belt length and centre distance with standard length, take-up allowances, wrap angle, the factors c1, c2 and c3, the required number of belts, belt speed, flex frequency and shaft load.
Power to be transmitted, speed and datum diameter of the small pulley, speed ratio or large-pulley diameter, optionally a provisional centre distance or an already chosen datum length, the belt section (SPZ, SPA, SPB, SPC, 19), the rated power per belt PN from the DIN 7753-2 power tables or the manufacturer's catalogue, and driven machine, driving machine and daily operating time for the service factor.
i = n1/n2, dwg = i·dwk; provisional datum length Lw ≈ 2e + 1.57·(dwg + dwk) + (dwg − dwk)²/(4e) with e = 0.9·(dwg + dwk), rounded up to the standard length per DIN 7753-1/ISO 4184; centre distance e = p + √(p² − q) with p = 0.25·Lw − 0.393·(dwg + dwk) and q = 0.125·(dwg − dwk)²; adjustment x ≥ 0.03·Lw, y ≥ 0.015·Lw; wrap angle from cos(β/2) = (dwg − dwk)/(2e) and wrap factor c1 per Table 1; service factor c2 per Table 2; length factor c3 per Tables 4/6/8/10/12; number of belts z = P·c2/(PN·c1·c3), rounded up; v = dwk·nk/19,100, fB = 2·v/Lw, F = 1,000·P/v, Fa = 1.5 to 2·F.
Worked example of DIN 7753-2 (page 9): lathe, three-phase motor with star-delta start, P = 22 kW, n1 = 2,940 min⁻¹, n2 = 735 min⁻¹, over 16 h/day, section SPZ, dwk = 140 mm, PN = 7.02 kW from Table 3. The calculator gives i = 4, dwg = 560 mm, provisionally e = 630 mm and Lw ≈ 2,429 mm, standard length 2,500 mm, e = 667 mm, x = 75 mm, y = 38 mm, β = 143°, c1 = 0.90, c2 = 1.3, c3 = 1.07 and z = 4.23 → 5 belts SPZ 2500 – exactly the result of the standard; in addition v = 21.6 m/s, fB = 17 s⁻¹ and F = 1,021 N.
Sources and limits: DIN 7753-2:1976-04 (formulae for speed ratio, datum length, centre distance, wrap angle, number of belts, belt speed, flex frequency, circumferential and shaft force; Table 1 wrap factor, Table 2 service factors, Tables 4, 6, 8, 10 and 12 length factors; worked example page 9), ISO 4184:2025 Table 3 (standard lengths of narrow V-belts), ISO 4183:2026 Table 4 (minimum datum diameters), Roloff/Matek, Maschinenelemente, 27th edition, TB 16-2 (reference limits vmax = 42 m/s, fB,max = 100 s⁻¹, imax = 10). Limits: open two-pulley drive without idler; the rated power per belt is an input from table or catalogue because it depends on section, diameter, speed, ratio and belt make; pretension and shaft load are approximations – belt manufacturers provide more precise values and tensioning methods.
The calculator determines, for an open two-pulley drive with narrow V-belts, the speed ratio, belt length and centre distance with standard length, take-up allowances, wrap angle, the factors c1, c2 and c3, the required number of belts, belt speed, flex frequency and shaft load.
DIN 7753-2 is the calculation standard for drives with narrow V-belts (sections SPZ, SPA, SPB, SPC and 19) on pulleys to DIN 2211. It answers how many belts of a section transmit a given power between two pulleys and fixes geometry and corrections for it: speed ratio and pulley diameters give belt length, centre distance and wrap angle; the rated power per belt determined under test-stand conditions (i = 1, β = 180°, reference length) is converted to the real drive with the wrap factor c1 and the length factor c3, while the service factor c2 covers the shocks of driven and driving machine and the daily running time. The calculator sits in the design step after the choice of section: once power, speeds and installation space are known and the section has been chosen per Figure 2 of the standard, it delivers the orderable belt set with centre distance and take-up allowances.
A V-belt drive is designed in three steps. First the design power P·c2 is formed and the section chosen from it per Figure 2 of DIN 7753-2 – SPZ for small powers at high speed, SPC for large powers at low speed. Then the pulley diameters are fixed: the small pulley as large as the space allows but at least per ISO 4183, the large one from the ratio, both rounded to DIN 2211 diameters. Only then does the calculation of this tool start: belt length, standard length, centre distance, factors and number of belts. The geometric steps can also be followed separately – with the belt length and centre distance and wrap angle calculators; the tension ratio the wrap angle physically permits is shown by the belt tension ratio (capstan equation) calculator, and the shaft load from the span forces by the pulley shaft load calculator.
Power and speeds: motor rating and speed from the nameplate, output speed from the task. Pulleys: datum diameters per DIN 2211 or ISO 4183; the small pulley sets belt speed and bending stress. Rated power per belt: from Tables 3, 5, 7, 9 and 11 of DIN 7753-2 for section, dwk, nk and ratio, or from the catalogue of the manufacturer – modern belts reach higher values than the 1976 tables, so the catalogue value is preferable. Service factor: driven machine, driving machine and daily operating time per Table 2; idlers, frequent starts and high starting torques call for a higher, self-chosen value. Centre distance and length: a provisional centre distance from the installation space or the existing belt length; otherwise the calculator takes e = 0.9·(dwg + dwk) like the example of the standard.
z = P · c2 / (PN · c1 · c3) → round up
i = n1/n2 = dwg/dwk · Lw ≈ 2e + 1.57·(dwg + dwk) + (dwg − dwk)²/(4e)e = p + √(p² − q), p = 0.25·Lw − 0.393·(dwg + dwk), q = 0.125·(dwg − dwk)²cos(β/2) = (dwg − dwk)/(2e) · c1 = f((dwg − dwk)/e) (Table 1) · c3 = f(Lw, section) (Tables 4–12)x ≥ 0.03·Lw, y ≥ 0.015·Lw · v = dwk·nk/19,100 · fB = 2·v/LwF = 1,000·P/v · Fa = (1.5 … 2)·F| Symbol / input | Meaning |
|---|---|
| P, PN, P·c2 | Power to be transmitted, rated power per belt under test-stand conditions and design power. |
| n1, n2, i | Speeds of driving and driven pulley and speed ratio. |
| dwk, dwg | Datum diameters of the small and large pulley per DIN 2211/ISO 4183. |
| e, Lw, β | Centre distance, datum length of the belt and wrap angle at the small pulley. |
| c1, c2, c3 | Wrap factor, service factor and length factor per the DIN 7753-2 tables. |
| z | Required number of belts (rounded up). |
| x, y | Adjustment of the centre distance for tensioning and for fitting. |
| v, fB, F, Fa | Belt speed, flex frequency, static circumferential force and shaft load. |
Power to be transmitted, speed and datum diameter of the small pulley, speed ratio or large-pulley diameter, optionally a provisional centre distance or an already chosen datum length, the belt section (SPZ, SPA, SPB, SPC, 19), the rated power per belt PN from the DIN 7753-2 power tables or the manufacturer's catalogue, and driven machine, driving machine and daily operating time for the service factor.
Enter power, speed and datum diameter of the small pulley and define the large pulley by the speed ratio or its diameter. Choose the section and take the rated power per belt from the standard or the catalogue for exactly this combination of section, dwk, nk and i. Assign driven and driving machine and the daily running time, or enter c2 yourself. Optionally enter a provisional centre distance or an existing belt length. The calculator returns the belt set, the final centre distance with adjustment and the operating figures; then round dwg to a standard pulley diameter and rerun the check.
Worked example of DIN 7753-2 (page 9): lathe, three-phase motor with star-delta start, P = 22 kW, n1 = 2,940 min⁻¹, n2 = 735 min⁻¹, over 16 h/day, section SPZ, dwk = 140 mm, PN = 7.02 kW from Table 3. The calculator gives i = 4, dwg = 560 mm, provisionally e = 630 mm and Lw ≈ 2,429 mm, standard length 2,500 mm, e = 667 mm, x = 75 mm, y = 38 mm, β = 143°, c1 = 0.90, c2 = 1.3, c3 = 1.07 and z = 4.23 → 5 belts SPZ 2500 – exactly the result of the standard; in addition v = 21.6 m/s, fB = 17 s⁻¹ and F = 1,021 N.
The calculated number of belts is always rounded up; the utilisation shows how much reserve the set has. If z is just above an integer, a larger pulley diameter or a longer standard length is worth a look, because both raise c1 or c3 and hence the rated power. The centre distance is not a free value: it follows from the chosen standard length, and the design must provide the adjustment x for tensioning (increase) and y for fitting (decrease). The wrap angle at the small pulley should stay above 120° if possible – the wrap factor drops quickly below. Belt speed and flex frequency are life quantities: above 42 m/s centrifugal force limits the power, above about 100 flexes per second the belt ages fast. The circumferential force and the shaft load estimated from it at 1.5 to 2 times serve the shaft and bearing design.
Power in kW, speeds in min⁻¹, diameters, lengths and centre distance in mm, angles in degrees, belt speed in m/s, flex frequency in s⁻¹, forces in N. The numerical-value equations of DIN 7753-2 (v = dwk·nk/19,100, F = 1,000·P/v) assume exactly these units.
The rated power per belt is determined on a test stand with equal pulleys (β = 180°) and a reference length. The wrap factor c1 accounts for the smaller friction area at a reduced wrap angle on the small pulley – physically the efficiency of the Eytelwein relation; Table 1 of the standard gives it over (dwg − dwk)/e, the calculator interpolates linearly. The length factor c3 captures the number of flexing cycles: a longer belt passes the pulleys less often, is flexed less and may transmit more power at the same life; hence c3 is below 1 for short belts and above 1 for long ones. The service factor c2 is a plant factor rather than a belt factor: it raises the power for shocks, overload at start-up and long running times. Reference values are 1.0 to 1.3 for light and 1.3 to 1.8 for very heavy drives.
Design of belt drives for pumps, fans, compressors, machine tools, conveyors, generators and mills; re-checking existing drives after a power increase or belt change; fixing centre distance and adjustment travel in the design; providing the shaft load for the shaft and bearing calculation.
DIN 7753-2:1976-04 (formulae for speed ratio, datum length, centre distance, wrap angle, number of belts, belt speed, flex frequency, circumferential and shaft force; Table 1 wrap factor, Table 2 service factors, Tables 4, 6, 8, 10 and 12 length factors; worked example page 9), ISO 4184:2025 Table 3 (standard lengths of narrow V-belts), ISO 4183:2026 Table 4 (minimum datum diameters), Roloff/Matek, Maschinenelemente, 27th edition, TB 16-2 (reference limits vmax = 42 m/s, fB,max = 100 s⁻¹, imax = 10). Limits: open two-pulley drive without idler; the rated power per belt is an input from table or catalogue because it depends on section, diameter, speed, ratio and belt make; pretension and shaft load are approximations – belt manufacturers provide more precise values and tensioning methods.
Common mistake: Do not confuse the outside diameter of the pulley with the datum diameter – the standard works with the datum diameter per DIN 2211. Do not skip correcting the rated power per belt for β = 180° and i = 1: c1 and c3 are not optional extras. Do not change the centre distance freely after the calculation without redetermining the belt length. Do not omit the adjustments x and y – without y the belt cannot be fitted without force, without x it cannot be retensioned. And at small wrap angles or more than eight belts reconsider the section or the drive type instead of just adding belts.
From the DIN 7753-2 power tables (Table 3 for SPZ, 5 for SPA, 7 for SPB, 9 for SPC, 11 for section 19) as a function of small-pulley datum diameter, speed and ratio – or, usually more favourable, from the belt manufacturer's catalogue for the actual make. The table values apply to β = 180° and the reference length; the calculator corrects with c1 and c3.
Because V-belts are only available in standard lengths. The provisional centre distance only serves to determine the length; after choosing the standard length the standard fixes the centre distance through e = p + √(p² − q), and the design must allow this value plus the adjustments x and y.
x ≥ 0.03·Lw is the adjustment for tensioning and later retensioning (increase of centre distance), y ≥ 0.015·Lw the travel for fitting the belt without force (decrease). With a fixed centre distance an idler is needed, which raises c2.
Table 1 of DIN 7753-2 goes down to 90° (c1 = 0.68). In practice the small pulley should be wrapped by at least 120°; below that the power drops quickly and slip and wear increase. Remedies are a larger centre distance or a smaller ratio per stage.
Both are life quantities. Narrow V-belts run up to about 42 m/s; above that centrifugal force reduces the contact pressure and the transmittable power. The flex frequency fB = 2·v/Lw should not exceed about 100 s⁻¹ – longer belts and larger pulleys lower it.
The procedure is the same, but table values, standard lengths and rated powers differ: classical V-belts to DIN 2215 follow DIN 2218, ribbed belts DIN 7867 or manufacturer data. This calculator contains the factors and standard lengths of the narrow sections SPZ, SPA, SPB, SPC and 19.