The calculator applies ISO 5295 to a two-pulley synchronous belt drive: from pitch, tooth numbers of pulleys and belt and the speed follow belt speed, pitch diameters and the centre distance – exactly via the involute function or approximately. From the manufacturer's allowable working tension Ta and linear mass m the basic power rating of the base-width belt is obtained and converted to the actual belt with the width factor kw and the teeth-in-mesh factor kz.
Trapezoidal synchronous belts of pitch codes MXL to XXH (base widths per ISO 5295 Table 1) or a free pitch; Ta and m are manufacturer data; two-pulley drive without idler.
Define pitch, tooth numbers and manufacturer data. The defaults follow the geometry of Roloff/Matek example 16.4 (T5, 38/114 teeth, 198 belt teeth).
For a two-pulley synchronous belt drive the calculator determines the power rating of the belt from the manufacturer values Ta and m, the centre distance from the number of belt teeth via the involute function, the teeth in mesh on the smaller pulley and the factors kz and kw – per equations (1) to (12) of ISO 5295.
Pitch Pb (via pitch code MXL to XXH or free), base width bso of the widest standard belt, actual belt width bs, tooth numbers z1, z2 and zb, speed of the smaller pulley, the allowable working tension Ta and the linear mass m of the base-width belt (manufacturer data) and optionally the required power for the utilisation.
Belt velocity v = ω·Pb·z1·10⁻³/(2π) (eq. 2), basic power rating Po = (Ta − m·v²)·v/1000 (eq. 1) and power rating P = kz·kw·(Ta − bs/bso·m·v²)·v/1000 (eq. 3) with kw = (bs/bso)^1.14 (eq. 12) and kz = 1 for zm ≥ 6, otherwise 1 − 0.2·(6 − zm) (eq. 10, 11). The centre distance follows from inv θ = π·(zb − z2)/(z2 − z1) and C = Pb·(z2 − z1)/(2π·cos θ) (eq. 5, 6); for z2/z1 near 1 the approximation eq. (7), (8) is used. Teeth in mesh zm = int[z1/2 − Pb·z1·(z2 − z1)/(2π²·C)] (eq. 9).
Roloff/Matek example 16.4: pitch 5 mm, z1 = 38, z2 = 114, zb = 198. The calculator gives C = 298.86 mm (book: 299 mm), zm = 16, v = 9.5 m/s at 3,000 rpm and a wrap angle of 156.6°; with Ta = 370 N, m = 0.1 kg/m, bso = 25.4 mm and bs = 12 mm follow kw = 0.43 and P ≈ 1.5 kW.
Sources and limits: ISO 5295:2023 eq. (1)–(12), Table 1; Roloff/Matek Maschinenelemente, example 16.4 and eq. (16.30); Gates/Optibelt timing belt catalogues for Ta and m.
For a two-pulley synchronous belt drive the calculator determines the power rating of the belt from the manufacturer values Ta and m, the centre distance from the number of belt teeth via the involute function, the teeth in mesh on the smaller pulley and the factors kz and kw – per equations (1) to (12) of ISO 5295.
ISO 5295 specifies for synchronous (timing) belts with trapezoidal tooth profile how the power rating of a belt is calculated from the manufacturer values and how the centre distance follows from tooth numbers and belt length. Unlike for V-belts there are no power tables in the standard: the manufacturer states, for the widest standard belt of each pitch (base width bso per Table 1), the allowable working tension Ta and the linear mass m; the standard supplies the procedure that turns them into the power rating for any belt width and speed. The calculator implements exactly that procedure: belt velocity, centrifugal deduction m·v², width factor kw, teeth in mesh zm and teeth-in-mesh factor kz, plus the exact centre distance via the involute function and, for comparison, the approximate formula.
A timing belt drive is designed in four steps. First the design power is formed from rated power and service factor and the pitch is chosen from the manufacturer selection chart (power over speed of the smaller pulley). Then the tooth numbers are fixed: z1 above the minimum tooth number of the profile, z2 = i·z1 rounded. In the third step the belt length is estimated from a provisional centre distance, rounded to a standard tooth number zb and the centre distance recalculated – this is where the calculator comes in, delivering the teeth in mesh at the same time. In the fourth step the belt width is chosen so that the power rating P covers the design power. If you only need the length from a given centre distance, use the Timing-belt pitch length and center distance calculator; the mesh geometry from the wrap angle is shown by the Timing-belt teeth in mesh calculator. For friction drives there is the Narrow V-belt drive to DIN 7753-2.
Pitch and base width: the pitch code sets Pb and bso per ISO 5295 Table 1 (the inch pitches 0.080 to 1.250 in of the codes are the classical values, not part of the standard); for metric profiles T, AT or HTD choose the free pitch and take bso from the catalogue. Tooth numbers: z1 from the minimum tooth number of the manufacturer and the desired belt velocity, z2 from the ratio, zb from the standard length series. Ta and m: given in the catalogues as allowable working tension and weight per metre for the base width – do not convert them for the chosen belt width, kw does that. Speed: motor speed if the smaller pulley drives. Required power: rated power times service factor (starting shocks, operating hours, speed-increasing ratio) per manufacturer catalogue.
P = kz · kw · (Ta − bs/bso · m · v²) · v / 1000
v = ω · Pb · z1 · 10⁻³ / (2π) · Po = (Ta − m·v²) · v / 1000inv θ = π · (zb − z2) / (z2 − z1) · C = Pb · (z2 − z1) / (2π · cos θ)C ≈ M + √(M² − (Pb·(z2 − z1)/π)²/8), M = Pb/8 · (2·zb − z1 − z2)zm = int[z1/2 − Pb · z1 · (z2 − z1) / (2π² · C)]kz = 1 (zm ≥ 6), kz = 1 − 0.2·(6 − zm) (zm < 6) · kw = (bs/bso)^1.14| Symbol / input | Meaning |
|---|---|
| Pb, bso, bs | Pitch, base width of the widest standard belt and actual belt width. |
| z1, z2, zb | Tooth numbers of the smaller and larger pulley and of the belt. |
| n1, ω, v | Speed and angular velocity of the smaller pulley, belt velocity. |
| Ta, m | Allowable working tension and linear mass of the base-width belt (manufacturer data). |
| Po, P | Basic power rating of the base-width belt and power rating of the actual belt. |
| zm, kz, kw | Teeth in mesh, teeth-in-mesh factor and width factor. |
| C, θ | Centre distance and auxiliary angle of the involute solution. |
Pitch Pb (via pitch code MXL to XXH or free), base width bso of the widest standard belt, actual belt width bs, tooth numbers z1, z2 and zb, speed of the smaller pulley, the allowable working tension Ta and the linear mass m of the base-width belt (manufacturer data) and optionally the required power for the utilisation.
Choose the pitch code or enter pitch and base width freely, give belt width, the three tooth numbers and the speed of the smaller pulley and take Ta and m from the manufacturer catalogue for the base width. With the optional required power the calculator shows the utilisation; if it exceeds 100 %, choose the next wider belt or the next larger pitch.
Roloff/Matek example 16.4: pitch 5 mm, z1 = 38, z2 = 114, zb = 198. The calculator gives C = 298.86 mm (book: 299 mm), zm = 16, v = 9.5 m/s at 3,000 rpm and a wrap angle of 156.6°; with Ta = 370 N, m = 0.1 kg/m, bso = 25.4 mm and bs = 12 mm follow kw = 0.43 and P ≈ 1.5 kW.
The power rating P is the power the chosen belt can transmit at the entered speed; the required power is the design power including the service factor, and the utilisation should stay below 100 %. If zm drops below 6, kz reduces the rating by 20 % per missing tooth – then a larger centre distance, a larger small pulley or a smaller ratio helps. The centre distance is not a free quantity but follows from the belt tooth number of the standard length series; the calculator reports the exact value and the approximation, which usually differ only by tenths of a millimetre. The usable tension Ta − m·v² shows how much of the allowable tension centrifugal force consumes at high speed.
Pitch, widths, diameters, centre distance and belt length in mm, speed in rpm, tension in N, linear mass in kg/m, power in kW, belt velocity in m/s, angles in degrees, torque in N·m. The ISO 5295 equations are numerical-value equations for exactly these units.
The allowable tension Ta applies when enough teeth carry the circumferential force. With fewer than six teeth in mesh the force concentrates on few teeth and the risk of tooth jumping rises – the teeth-in-mesh factor kz takes back 20 % of the rating per missing tooth. The width factor kw transfers the base-width values to the actual width; the exponent 1.14 instead of 1 reflects that narrow belts have proportionally more edge region and therefore carry less than linearly. Per ISO 5295, kw is rounded to two decimals, which the calculator adopts. The centrifugal share m·v² is scaled to the actual width with bs/bso in eq. (3); the approximation eq. (4) applies it with the base width and therefore differs slightly.
Design of slip-free drives for machine tool axes, printers and handling devices, camshaft and balance shaft drives, pumps and fans with a fixed speed ratio; re-checking existing timing belt drives after a power increase or belt change; fixing centre distance and belt width in the design.
ISO 5295:2023 eq. (1)–(12), Table 1; Roloff/Matek Maschinenelemente, example 16.4 and eq. (16.30); Gates/Optibelt timing belt catalogues for Ta and m.
Common mistake: Do not enter Ta and m for the actual belt width – the standard refers both to the base width bso, otherwise kw is applied twice. Do not confuse the belt tooth number zb with the belt length in mm. For z2/z1 near 1 the involute formula is numerically unfavourable; the calculator then switches to the approximation. Do not fix the centre distance without tensioning and fitting travel: timing belts need a defined pretension that the manufacturer derives from the circumferential force.
From the belt manufacturer catalogue: it lists the allowable working tension and the weight per metre for each pitch, usually for the widest standard belt or for a reference width. The calculator expects the values for the base width bso; if the catalogue states them for another reference width, enter that as bso.
Because timing belts are only available in standard tooth numbers and do not stretch. The standard determines the centre distance exactly via the involute function inv θ = π·(zb − z2)/(z2 − z1); for z2/z1 near 1 it recommends the approximate formula, for large ratios the exact form.
At least six – below that kz reduces the rating by 20 % per missing tooth. At high ratios and short centre distances zm drops quickly; a larger centre distance, more teeth on the small pulley or an idler on the slack side help.
The ISO 5295 procedure is profile-independent, but the standard itself covers the trapezoidal inch pitches MXL to XXH. For metric profiles choose the free pitch and take Ta, m and bso from the manufacturer catalogue; manufacturer catalogues often use their own power tables, which govern in case of deviation.
Both give the rating of the belt of width bs. Eq. (3) scales the centrifugal share m·v² with bs/bso to the actual width, eq. (4) simply multiplies the basic power rating Po by kz·kw. At low speeds both are practically equal; at high speeds eq. (3) is the more accurate form.