Star-Delta Starting Calculator
Starting current and torque with a star-delta starter compared with direct-on-line. With the formula, a worked example and typical values.
Try your own numbers
Estimate only. Not engineering or safety advice. Check the result against the applicable standard and the equipment data, and have a competent engineer review it before it is relied on. Terms of use.
Open in the calculator with these values
About this calculator
This page calculates DOL starting current, star starting line current, DOL starting torque and 1 more result from motor rated current, locked-rotor current ratio, motor rated torque, locked-rotor torque ratio and 1 more input. Change any value or its unit and the result updates. The steps below show the working for the default values, so you can check each line against your own method.
Limits of this calculator
Star-delta cuts both current and torque to one third. It only suits loads that start with low torque, such as unloaded fans and pumps with a closed valve.
Cross-check: 6 reference cases, calculated from textbook formulas coded separately from the engine by the same author, agree with this calculator. This is not an independent review.
Verification status: Engineering reference
Engineering reference. Formula and method documented and tested against separately coded reference calculations. Not yet Verified: the evidence listed on this page is still needed.
What this calculator checks
- The arithmetic of the published formula for the values you entered, in the units shown.
What remains unverified
- That the inputs suit your application. Take ratings, resistances and constants from the manufacturer data sheet or project specification.
Verification register entry
| Calculation author | Rahul Sharma (author) |
|---|---|
| Technical review | No independent technical review has been carried out |
| Individual professional approval | Not recorded |
| Formula reference | not recorded |
| Standard and edition | IEC 60034-12, 2024 Ed 4.0 |
| Standard review state | Public-scope screened; licensed clause review still pending |
| Scope-screening note | Starting performance for single-speed three-phase cage induction motors is relevant. The one-third current/torque relationships are idealised star-delta estimates; actual motor design, transition and load torque affect performance. |
| Cross-check test cases | 6 reference vectors (tests/reference_vectors.json) |
| Review date | not recorded |
| Next review date | not recorded |
| Status | Engineering reference |
Needed before this calculator can be marked Verified: reviewer name, qualification and review date; licensed clause-by-clause standard review; exact formula reference; formula source (textbook or standard); next review date.
Formula
Worked example
| Input | Value |
|---|---|
| Motor rated current | 100 A |
| Locked-rotor current ratio (ILR / In) | 6 |
| Motor rated torque | 500 N·m |
| Locked-rotor torque ratio (TLR / Tn) | 1.5 |
| Load torque at start | 150 N·m |
- IDOL = 6 × 100 = 600 A
- Istar = 600 / 3 = 200 A
- TDOL = 1.5 × 500 = 750 N·m, Tstar = 250 N·m
Assumptions
- Motor is delta-connected at its rated line voltage
- Supply voltage stays constant
- Switching transient peak is not included
Star-delta cuts both current and torque to one third. It only suits loads that start with low torque, such as unloaded fans and pumps with a closed valve.
Inputs and results
| Input | Unit | Allowed or shown | Note |
|---|---|---|---|
| Motor rated current | A | greater than 0 A | |
| Locked-rotor current ratio (ILR / In) | (number) | 1 or more | From the motor data sheet |
| Motor rated torque | N·m | greater than 0 N·m | |
| Locked-rotor torque ratio (TLR / Tn) | (number) | greater than 0 | |
| Load torque at start | N·m | 0 N·m or more |
| Result | Unit | Allowed or shown | Note |
|---|---|---|---|
| DOL starting current | A | Shown to 0 decimal places | |
| Star starting line current | A | Shown to 0 decimal places | |
| DOL starting torque | N·m | Shown to 0 decimal places | |
| Star starting torque | N·m | Shown to 0 decimal places |
How it is calculated
Each input is converted to the base unit of its quantity, the formula above is applied in the order shown in the worked example, and each result is shown in the unit you choose. Results are held at full precision and rounded only for display, except where a step selects a standard size, as the worked example shows. A value outside its allowed range is refused with a message instead of giving a result.
How the result changes with motor rated current
| Motor rated current (A) | DOL starting current (A) | Star starting line current (A) | DOL starting torque (N·m) |
|---|---|---|---|
| 10 | 60 | 20 | 750 |
| 25 | 150 | 50 | 750 |
| 50 | 300 | 100 | 750 |
| 100 | 600 | 200 | 750 |
| 200 | 1,200 | 400 | 750 |
| 400 | 2,400 | 800 | 750 |
| 1,000 | 6,000 | 2,000 | 750 |
Other inputs are the same as in the worked example above.
Standards and further reading
- IEC 60034-1 (rotating electrical machines, rating and performance)
- IEC 60034-30-1 (efficiency classes)
Where the motor nameplate or data sheet gives a value, use it in place of a calculated one. These are named as background reading. Elecmetric does not embed clause text or rating tables, and the reviewer record for this calculator is separate from this list.
Frequently asked questions
What do I need to enter?
Enter motor rated current, locked-rotor current ratio (ILR / In), motor rated torque, locked-rotor torque ratio (TLR / Tn) and load torque at start. Change the unit of a value with its selector and the result stays the same.
What does this calculator assume?
Motor is delta-connected at its rated line voltage. Supply voltage stays constant. Switching transient peak is not included.
Which calculators should I use next?
Common next steps are Motor Starting Current and Motor Starting Voltage Dip. The related links at the bottom of this page open them.
How accurate are the results?
Every figure comes from the same tested engine as the Elecmetric calculators and is meant for estimating. 6 reference cases, calculated from textbook formulas coded separately from the engine by the same author, agree with this calculator. This is not an independent review. Check design values against the standard and the equipment data you work to.
Formula guides and reference
Longer explanations with worked examples and tables, written for the same topic.
- Star-Delta Conversion Formulas for Resistors: Star-delta (wye-delta) conversion formulas for resistors or impedances in both directions, equal-resistor shortcut
- Motor Starting Formulas: DOL, Star-Delta: Motor starting formulas for direct-on-line, star-delta, autotransformer and soft starter current and torque
- Soft Starter and VFD Sizing Formulas: Soft starter and VFD formulas: start current and torque at a reduced voltage, drive input power, kVA and current
More Motor Engineering calculatorsAll engineering calculatorsStar-Delta Starting in Elecmetric