Motor starting calculator
Pick a motor, a starting method and a load, and see the whole starting transient play out — speed, line current, torque and winding temperature, all plotted against time. Compare DOL, Star-Delta, Autotransformer, Soft Starter and VFD starting on the exact same motor and load to see the real trade-off between inrush current, starting torque and how long the motor takes to get to speed.
Speed, current & torque vs. time
Winding temperature vs. time
Shows the starting transient plus 10 minutes of continuous rated-load running afterward, so you can see whether temperature is still climbing toward a steady state or has settled — see the theory section below for the model behind it.
How this calculator works
This simulates a motor's starting transient — the few seconds (or tens of seconds) between a start command and reaching full speed — for whichever starting method you pick, against your motor's own torque-slip characteristic and your load's own torque-speed shape. It doesn't select a starting method for you; it shows you what each one actually does to speed, current, torque and winding temperature, on the same motor and load, so you can compare them directly.
The torque-slip curve
Every motor datasheet gives three points on its torque-slip curve: starting torque (Tst, at slip s=1, rotor locked), breakdown/pull-out torque (Tmax, the highest torque the motor can produce, at some intermediate slip) and rated torque (Tn=1 by definition, at rated slip sn). A single classic Kloss equation (T/Tmax = 2 / (s/smax + smax/s)) can't be forced through all three independently — it only has one free parameter (smax) once Tmax is fixed. This calculator solves for smax from the rated point (so the curve passes exactly through Tn at sn), uses that Kloss curve from synchronous speed down to breakdown slip — the region that actually matters for acceleration, and where the classic curve is most trustworthy — and then blends linearly from breakdown torque to the catalogue starting torque for the remaining region down to s=1. That's a deliberate engineering approximation: a real cage rotor's torque above breakdown slip is bent by rotor current-displacement (skin) effects that a straight line doesn't capture, but it's a defensible stand-in without asking for rotor bar geometry the datasheet doesn't give. Motor current follows a similar piecewise-linear model between no-load current (assumed ~35% In), rated current at sn, and locked-rotor current (Ist) at s=1.
Kloss (0 ≤ s ≤ smax): T/Tmax = 2 / (s/smax + smax/s)
Linear blend (smax ≤ s ≤ 1): T = Tmax + (s−smax)/(1−smax) · (Tst−Tmax)
Breakdown slip (solved from the rated point): smax = sn · (Tmax/Tn + √((Tmax/Tn)²−1))
Load torque and the equation of motion
Three load shapes are offered: fan/pump (torque proportional to speed squared — the standard centrifugal-load characteristic, and the one most relevant to CloudAir's own focus), constant torque (conveyors, crushers, positive-displacement loads) and linear (torque proportional to speed — less common, included for completeness). Speed is found by integrating the equation of motion, Jtotal·dω/dt = Tmotor−Tload, numerically (2 ms steps — small enough that the torque-slip curve's steepness near the operating point doesn't make the integration ring) from standstill, where Jtotal is motor rotor inertia plus load inertia referred to the motor shaft — direct coupling is assumed; a belt or gear ratio between motor and load isn't modelled. If motor torque never exceeds load torque by more than a hair across the whole speed range, the motor can't accelerate past that point — the calculator detects this and reports a stall rather than showing a nonsensical result.
Load inertia specifically is worth double-checking against a real fan datasheet before trusting the starting time or thermal numbers: this calculator's auto-estimate scales it off the motor's own rotor inertia by a fixed, deliberately conservative multiple, but the real ratio between a fan wheel's inertia and its motor's varies enormously — a large-diameter centrifugal fan wheel can easily carry many times its motor's rotor inertia, and the multiple that's actually right for your fan isn't something this calculator can know without a real inertia figure. Because starting time scales directly with total inertia (double J → roughly double the starting time, for a similar torque margin), this is one of the highest-leverage fields to get right.
The five starting methods
Direct-on-line (DOL) applies full rated voltage from t=0 — simplest, cheapest, and the highest inrush current and starting torque of the five. Star-Delta (Y-Δ) connects the motor windings in star for an initial period (phase voltage reduced to 1/√3 of rated), which — because motor torque scales with voltage squared and, for a star connection, line current equals phase current — cuts both starting torque and line current to almost exactly 1/3 of their DOL values, then switches to delta (full voltage) after the time you set; this is an exact result of the star/delta relationship, not an approximation. Autotransformer starting feeds the motor through a tapped transformer at a reduced voltage (typically 50/65/80% of rated); motor-side torque and current follow the usual V² and V scaling, but — because an (ideal) transformer's apparent power balances between primary and secondary — the current the supply sees is reduced by another factor of the tap ratio, so line current scales with the tap ratio squared. That's the reason autotransformer starting draws less line current than a soft starter for the same reduction in motor voltage. Soft starters ramp the applied voltage linearly from a starting level up to full voltage over a set time using thyristor phase control — since there's no transformer stage, line current here equals motor current (only the plain V scaling applies, not V²). VFDs are modelled differently from the other four: instead of applying a fixed or ramping voltage to a motor running on its natural torque-slip curve, the calculator advances a commanded frequency toward rated over your set ramp time, and holds torque (and current) at your set current limit while the motor is still catching up to that commanded frequency — the standard behaviour of a closed-loop V/f or vector drive during a current-limited ramp. Once the motor catches up to the commanded frequency, torque and current settle to whatever the load needs at that speed. This means a VFD start looks qualitatively different from the other four on the chart: roughly constant torque and current during the ramp, rather than a curve that rises and falls with slip. Critically, the commanded frequency isn't a fixed ramp the calculator forces speed to follow regardless of whether the motor physically can: it only keeps advancing while the motor is within a small slip margin of it, and holds steady (freezes) once the motor falls further behind than that — the same current-limit stall-prevention behaviour a real drive uses rather than pushing the commanded frequency further and further ahead of a motor that can't keep up. Set a ramp time too aggressive for the motor/load combination and the calculator will show the commanded frequency stalling and waiting rather than racing to 100% on schedule while the motor lags increasingly far behind — the actual time to reach full speed then runs longer than the ramp time you set, which is exactly what a current-limited real drive would do too.
One caveat on VFD line current specifically: the current-limit value plotted is the motor-side (drive output) current. The current the supply actually draws (the drive's rectifier input) is usually meaningfully lower, especially at low output frequency — one of the real advantages of VFD starting — but modelling that needs the drive's DC-link and rectifier behaviour, which is outside what this calculator attempts; treat the VFD current curve as motor current, not supply current.
Winding temperature
The temperature chart covers the starting transient plus the following 10 minutes of continuous running at rated load, so you can see not just how hot the start itself gets but whether the motor is still climbing toward a steady operating temperature afterward or has already settled. It's built from the standard first-order heating/cooling equation, d(rise)/dt = (target−rise)/τ, where target at any instant is the motor's rated continuous temperature rise for its insulation class scaled by (line current/In)², and τ is the thermal time constant you enter. During the starting transient itself — typically seconds, much shorter than τ — almost none of that heat has time to leave through the motor's normal cooling path, so this reduces to the same adiabatic, integrate-I²t behaviour a pure adiabatic model would give; over the following minutes, as current drops to its rated running value, the same equation correctly relaxes the temperature toward the rated continuous rise rather than leaving it frozen wherever the starting transient happened to end. Class B/F/H rated continuous rises are 80/105/125 K per IEC 60034-1. The thermal time constant is a stand-in for the winding's thermal mass and isn't something most datasheets state outright; 15-45 minutes is a typical range for industrial motors, longer for larger frames. This is deliberately a rough estimate, not a thermal model of the motor's actual insulation system — it ignores where in the winding heat concentrates, ambient temperature effects beyond the IEC reference ambient, and assumes the post-start load is held at exactly 100% of rated current throughout the 10-minute window rather than whatever the real duty cycle is. The summary table's "during start" figure is the rise at the moment the starting transient ends, not the 10-minute figure the chart continues to show — that's the number to check against a starting-related thermal limit; the chart is for judging longer-term duty.
This page checks one motor and one starting method at a time. CloudAir's selection programs size motors and drives across a whole product range automatically. See how CloudAir handles it →