There is no single insulation resistance formula. There are five, and people mix them up constantly — using the measurement equation when they need the correction equation, or applying an acceptance formula built for 1950s asphalt to a modern epoxy winding.
This page lays them out one at a time: what each equation is for, what the symbols mean, what units bite you, and a worked number for each.
Table of Contents
1. The measurement formula
IR = V / I
Ohm’s law, applied to the leakage path. Your megger applies a DC voltage across the insulation, measures the tiny current that gets through, and divides.
| Symbol | Meaning | Unit |
|---|---|---|
| IR | Insulation resistance | MΩ |
| V | Applied DC test voltage | volts |
| I | Total measured current | microamperes (µA) |
The unit trap. Volts divided by microamps gives megohms directly. 500 V ÷ 1 µA = 500 MΩ. Put the current in milliamps by mistake and you are off by a factor of 1000. This is the single most common arithmetic error in insulation calculations.
IEEE 43 writes it with the time subscript, because when you read matters:
IR_t = E(t) / I(t)
The current is not constant — it decays as the insulation polarises. IR at 15 seconds and IR at 60 seconds are different numbers from the same healthy winding. The standard convention: subscripts 1–10 mean minutes, 15 and above mean seconds. So IR₁ is the one-minute reading, IR₆₀ is the sixty-second reading — the same instant, written two ways.
Worked example: 500 V applied, megger shows 2.5 µA at 60 s. IR₁ = 500 / 2.5 = 200 MΩ
2. The geometry formula
R = ρL / A
Why a long cable reads lower than a short one made of the same material.
| Symbol | Meaning |
|---|---|
| ρ | Resistivity of the insulating material |
| L | Length of the leakage path |
| A | Cross-sectional area of that path |
The practical consequence: insulation resistance is inversely proportional to the conductor surface area, and proportional to insulation thickness. Two identical cables in parallel read half the resistance of one. A 500 m run reads roughly half a 250 m run.
This is why cable IR is often quoted normalised per kilometre:
IR (MΩ·km) = IR_measured (MΩ) × length (km)
A 400 MΩ reading on a 500 m cable is 400 × 0.5 = 200 MΩ·km. Compare that against the spec, not the raw display value. Comparing raw readings across different cable lengths is meaningless.
For a single-core cable, the geometry resolves to:
R = (ρ / 2πL) × ln(D/d)
where D is the insulation outer diameter and d the conductor diameter.
3. The temperature correction formula
This is the one that gets botched most often, including in published field guides.
R₄₀ = K_T × R_measured
R₄₀ is the resistance referred to the 40 °C reference temperature. K_T is the correction factor. And the direction matters:
Insulation resistance falls as temperature rises. So a reading taken on a cold winding must be corrected downward. A reading taken hot must be corrected upward.
If your correction makes a cold reading bigger, you have the formula inverted. Sanity-check every time.
Thermoplastic systems (asphaltic-mica, shellac — pre-1960s)
K_T = 0.5^((40 − T) / 10)
Equivalently, K_T = 2^((T − 40)/10). Resistance halves for every 10 °C rise. This is the origin of the “halve it per 10 degrees” rule of thumb.
Thermosetting systems (epoxy, polyester — post-1960s)
IEEE 43-2013 gives two exponential fits, because these materials do not follow a clean halving law:
For 40 °C < T < 85 °C: K_T(T) = exp[ −4230 × (1/(T + 273) − 1/313) ]
For 10 °C < T < 40 °C: K_T(T) = exp[ −1245 × (1/(T + 273) − 1/313) ]
Both are approximations, and IEEE notes they can drift badly outside 10–60 °C.
The values, computed
| Winding temp (°C) | K_T thermoplastic | K_T thermosetting |
|---|---|---|
| 10 | 0.125 | 0.7 |
| 20 | 0.25 | 0.8 |
| 30 | 0.5 | 0.9 |
| 40 | 1.0 | 1.0 |
| 50 | 2.0 | 1.5 |
| 60 | 4.0 | 2.3 |
| 70 | 8.0 | 3.3 |
| 80 | 16.0 | 4.6 |
Do not use the halving rule on a modern winding. At 60 °C the thermoplastic factor is 4.0 and the thermosetting factor is 2.3. Apply the wrong one to an epoxy-mica motor and you overstate the corrected resistance by nearly 75%.
Worked example: epoxy-mica motor, 300 MΩ measured at 60 °C. Thermosetting K_T = 2.3 → R₄₀ = 300 × 2.3 = 690 MΩ Wrong (thermoplastic) K_T = 4.0 → 1200 MΩ. A number that does not exist.
Where correction stops working: below the dew point. The K_T equations were derived on clean, dry bars. Once moisture is condensing on the surface, no correction factor rescues the reading. Fall back on the machine’s own history. Details in the temperature correction guide.
4. The ratio formulas
Neither needs temperature correction. Both readings sit at essentially the same winding temperature, so K_T cancels in the division. That is the whole point of a ratio.
Polarization index: PI = IR₁₀ / IR₁
Ten-minute reading over one-minute reading. Minimum 2.0 for Class B insulation and above, 1.5 for Class A.
Dielectric absorption ratio: DAR = IR₆₀ₛ / IR₃₀ₛ
Sixty seconds over thirty. The quick version when a ten-minute test is not practical.
Worked example: IR₁ = 150 MΩ, IR₁₀ = 450 MΩ. PI = 450 / 150 = 3.0. Clean and dry.
The catch: above 5000 MΩ at one minute, the currents involved drop into the sub-microamp range and the ratio becomes noise. IEEE 43 says the PI is not a reliable tool up there. A motor at 8 GΩ with a PI of 0.9 is a healthy motor with a meaningless ratio. See DAR vs PI.
5. The acceptance formulas
These answer a different question: not what is the resistance, but is it good enough. IEEE 43-2013 Table 4 gives three, and which one applies depends on the machine, not on preference.
| Formula | Applies to |
|---|---|
| IR₁ min = kV + 1 MΩ | Windings built before roughly 1970, and all field windings |
| IR₁ min = 100 MΩ | AC form-wound windings built after roughly 1970 |
| IR₁ min = 5 MΩ | Random-wound stators, form-wound below 1 kV, DC armatures |
kV is the rated line-to-line voltage in kilovolts (line-to-ground for single-phase; rated DC voltage for DC machines and field windings).
The kV + 1 formula is the famous one, and it is the one most often misapplied. It was calibrated for thermoplastic insulation. Run it on a modern 4160 V epoxy-mica motor and you get 5.16 MΩ — roughly twenty times below the 100 MΩ that actually applies. Full breakdown on the motor megger value page.
Every one of these minimums is compared against the temperature-corrected IR₁, never the raw display value.
Putting it together
A 6.6 kV form-wound motor, epoxy-mica, tested at 2500 V DC. Megger reads 8 µA at 60 seconds. Winding at 50 °C.
- Measure: IR₁ = 2500 / 8 = 312.5 MΩ
- Correct: thermosetting K_T at 50 °C = 1.5 → R₄₀ = 312.5 × 1.5 = 469 MΩ
- Compare: post-1970 form-wound, minimum = 100 MΩ → passes with margin
- Confirm with the ratio: if IR₁₀ = 1100 MΩ, PI = 1100 / 312.5 = 3.5 → well above the 2.0 minimum
Both criteria clear. The machine is fit to energise.
Note what would have happened if you had skipped step 2 in the other direction — a cold winding at 20 °C reading 130 MΩ looks like a pass, until K_T = 0.8 brings it to 104 MΩ. Still passing, but barely, and the raw number hid that.
Quick reference
| Purpose | Formula |
|---|---|
| Measurement | IR = V / I (volts ÷ µA = MΩ) |
| Geometry | R = ρL / A |
| Cable normalisation | IR (MΩ·km) = IR_measured × length in km |
| Temperature correction | R₄₀ = K_T × R_measured |
| K_T, thermoplastic | 0.5^((40 − T)/10) |
| K_T, thermosetting (10–40 °C) | exp[−1245 (1/(T+273) − 1/313)] |
| K_T, thermosetting (40–85 °C) | exp[−4230 (1/(T+273) − 1/313)] |
| Polarization index | PI = IR₁₀ / IR₁ |
| Dielectric absorption ratio | DAR = IR₆₀ₛ / IR₃₀ₛ |
| Minimum IR — pre-1970 and field windings | kV + 1 MΩ |
| Minimum IR — modern form-wound AC | 100 MΩ |
| Minimum IR — random-wound, <1 kV, DC armature | 5 MΩ |
FAQ
What is the basic insulation resistance formula?
IR = V / I. Applied DC test voltage divided by the leakage current it drives. Volts over microamps gives the answer directly in megohms.
What is the formula for temperature correction of insulation resistance?
R₄₀ = K_T × R_measured, where K_T comes from the curve for your insulation type. For thermoplastic insulation, K_T = 0.5^((40 − T)/10). Modern epoxy windings use the exponential thermosetting equations instead — the halving rule over-corrects them badly.
Why does insulation resistance decrease with temperature?
Heat supplies thermal energy that frees additional charge carriers in the dielectric. More carriers means more current at the same applied voltage, so lower resistance. This is the opposite of what metals do, where resistance rises with temperature.
What is the kV + 1 formula?
An acceptance threshold from IEEE 43: minimum IR₁ in megohms equals rated kV plus 1. It applies only to pre-1970 windings and field windings. Modern form-wound machines use a flat 100 MΩ minimum instead.
Does the polarization index need temperature correction?
No. Both readings are taken at effectively the same winding temperature, so the correction factor cancels in the ratio. The one exception: a winding cooling rapidly from high operating temperature during the ten-minute test can produce an artificially high PI.