Core Loss Calculator (Steinmetz)

Pᵥ = k·f^α·B^β from a ferrite data sheet, times the effective core volume, with the copper loss and a temperature rise beside it — and, because this is where the factor-of-a-thousand errors live, an explicit statement of which units your three constants are in.

Last updated 24 Sep 2026

Core loss, copper loss and the temperature rise

k, α, β + f, B, Vₑ → loss

Frequency unit your constants are quoted inThis is about the CONSTANTS, not about your converter. Get it wrong and the answer is out by 1000^α — about a factor of 5,000 at α = 1.25.

Flux density unit your constants are quoted inGet this wrong and the answer is out by 1000^β — about a factor of 30 million at β = 2.5.

Loss density unit your constants are quoted in1 mW/cm³ is exactly 1 kW/m³, so those two never need converting between them. W/m³ is a thousand times smaller.

Steinmetz coefficient kFitted here to the three loss figures Ferroxcube specifies for 3C90 at 100 °C, in mW/cm³ with f in Hz and B in T. Your data sheet’s own constants go here instead. Use the figures from your part’s datasheet; typical values vary widely between manufacturers.

Frequency exponent αTypically 1.1 to 1.8 for a power ferrite. Two loss figures at the same flux density and different frequencies give it: α = ln(P₂/P₁) ÷ ln(f₂/f₁).

Flux density exponent βTypically 2.2 to 3.0. Two loss figures at the same frequency and different flux densities give it: β = ln(P₂/P₁) ÷ ln(B₂/B₁).

Lowest frequency your constants were fitted over (kHz)Steinmetz constants are only valid over the band they were fitted on. Ferroxcube publishes separate rows for 3F3 at 100–300, 300–500 and 500–1000 kHz precisely because one set will not stretch.

Highest frequency your constants were fitted over (kHz)

Switching frequency (kHz)The frequency the flux actually swings at. In a push-pull or full bridge the core sees the switching frequency even though each switch runs at half of it.

Peak flux density B̂ (mT)PEAK, not peak-to-peak. The classic Steinmetz equation is written for a sinusoid of amplitude B̂; for a converter waveform the peak is half the swing, ΔB/2.

Effective core volume Vₑ (mm³)From the core data sheet. 11,500 mm³ for an ETD 39/20/13 core set, which is the default here. Use the figures from your part’s datasheet; typical values vary widely between manufacturers.

Excitation waveformThe Steinmetz equation is defined for a sinusoid. A converter applies a square voltage, so the flux is a triangle, and the loss is different — lower at 50% duty, higher at every other duty.

Duty cycle of the square-wave excitation (%)Only used for the iGSE option. 50% is the symmetric case; the further from 50% the more the flux ramps in one direction and the higher the loss.

Winding resistance at the operating temperature (Ω)The AC resistance, not the DC resistance, if the winding is thick compared with a skin depth.

Winding RMS current (A)RMS, including the ripple. For a transformer, add the two windings’ losses separately and enter the total as one equivalent I²R.

Temperature-rise modelThe first two are empirical fits to natural convection from a wound assembly and they disagree with each other by a good margin — see the table below. Use a measured thermal resistance if your core set publishes one.

Surface area of the wound assembly (cm²)About 31 cm² for a bare ETD 39/20/13 core set, more once it is wound. This is an estimate, not a data sheet figure: McLyman’s core tables list a surface area for each core, and measuring your own assembly is better than either.

Thermal resistance, core to ambient (°C/W)Only used by the third model. A wound ETD 39 in still air is of the order of 15–20 °C/W; a core set data sheet sometimes publishes it. Use the figures from your part’s datasheet; typical values vary widely between manufacturers.

Ambient temperature (°C)Inside the enclosure, not the room.

A geometry rather than a circuit: the cross-section of an E-core pair with the winding in both windows, and the closed flux path the Steinmetz equation is integrated over. The effective volume Vₑ on the data sheet is that path's length times its area, and the loss density multiplied by it is the whole core loss. The panel on the right is the flux waveform the selected excitation implies: a sine for the classic equation, a triangle for the iGSE. The numbers underneath are this page's own.

920mWExample

the 3C90 constants fitted below, 100 kHz at 100 mT peak in an ETD 39/20/13’s 11,500 mm³ of effective volume, with 0.10 Ω carrying 3 A rms

The equation, its units, and the square-wave correction

Pᵥ = k · f^α · B̂^β (sinusoidal excitation only)
P_core = Pᵥ · V_e
k_i = k ÷ [ 2^β+1 · π^α−1 · (0.2761 + 1.7061 ÷ (α + 1.354)) ]
iGSE, triangular flux: Pᵥ = k_i · (ΔB)^β · f^α · [ D^1−α + (1−D)^1−α ]
ΔT = 450 · (P ÷ A)^0.826 (P in W, A in cm²)

k, alpha, beta: curve-fit constants with units. k carries whatever units the fit’s axes had, which is why this page asks
B peak: the amplitude of the flux swing, not the swing. For a converter, half of ΔB
Ve: the effective core volume from the core data sheet — the volume the effective path length and area imply, not the volume of ferrite you could weigh
ki: the iGSE constant, fixed by requiring the iGSE to give the Steinmetz answer for a sinusoid
D: the duty cycle. At D = 0.5 the triangular waveform loses a few per cent LESS than a sinusoid of the same peak; away from 0.5 it loses more

Worked example

the 3C90 constants fitted below, 100 kHz at 100 mT peak in an ETD 39/20/13's 11,500 mm³ of effective volume, with 0.10 Ω carrying 3 A rms
In SI the constants are k = 14.6322 with Pᵥ in W/m³, f in Hz and B in T; the same fit with Pᵥ in mW/cm³, f in kHz and B in mT is k = 2.6763 × 10⁻⁶ — the same physics, a factor of 5.467 million apart
Pᵥ = 14.6322 × (100,000 Hz)^1.2459 × (0.1 T)^2.4919 = 80 kW/m³, which is 80.0 mW/cm³ — and that is the data sheet's own 80 kW/m³ figure, because the constants were fitted to reproduce it
Times 11,500 mm³ of effective volume, the core loses 920 mW; the winding loses 3² × 0.10 = 900 mW, so the assembly dissipates 1.82 W in total
Driven by a square voltage at 50% duty rather than a sine, the iGSE puts the core loss at 883.1 mW instead — 4.0% lower, and the gap widens fast, in the other direction, as the duty moves away from a half
1.82 W over 31 cm² is 0.0587 W/cm², so McLyman's fit gives a rise of 43.3 °C and a core at 68.3 °C

Published 3C90 constants against Ferroxcube’s own 3C90 data sheet

Ferroxcube’s own application note *Design of Planar Power Transformers* publishes Cm = 3.2×10⁻³, x = 1.46, y = 2.75 for 3C90 over 20–200 kHz, in mW/cm³ with f in Hz and B in T. Evaluated here at the three loss figures the 3C90 material specification itself gives, it runs 26 to 70% high. Both documents are genuine; the fit was simply made over a different range and against different measurements. That is the reason this page’s defaults are fitted to the data sheet’s own three points instead — three points, three unknowns, an exact fit.
Condition (100 °C)	Data sheet Pᵥ	Published fit, Cm 3.2×10⁻³, x 1.46, y 2.75	Difference
25 kHz, 200 mT	80 kW/m³	101 kW/m³	+26%
100 kHz, 100 mT	80 kW/m³	114 kW/m³	+42%
100 kHz, 200 mT	450 kW/m³	764 kW/m³	+70%

Fitting your own constants from two or three data sheet figures

Three data sheet figures give an exact fit and cost nothing. Doing this at your own operating point is worth far more than any published set of constants, because it removes both the frequency-range and the temperature question at once.
You have	You get	How
Two losses at the same B, different f	α	α = ln(P₂/P₁) ÷ ln(f₂/f₁). For 3C90: ln(450/80) ÷ ln(100/25) = 1.246
Two losses at the same f, different B	β	β = ln(P₂/P₁) ÷ ln(B₂/B₁). For 3C90: ln(450/80) ÷ ln(200/100) = 2.492
Any one loss figure, plus α and β	k	k = P ÷ (f^α · B^β), in whatever units you read P, f and B in
More than three figures	a least-squares fit	fit ln P = ln k + α ln f + β ln B; the residuals tell you whether one power law covers your range at all

Published Steinmetz constants for Ferroxcube grades

All from *Design of Planar Power Transformers*, in mW/cm³ with f in Hz and B in T, and each with its own frequency band — 3F3 needs three separate rows to cover 100 kHz to 1 MHz, which is the clearest possible statement that one power law does not describe a ferrite everywhere. The same note gives a temperature factor (ct₀ − ct₁T + ct₂T²) that equals 1 at 100 °C.
Grade	Band	Cm	x (α)	y (β)
3C30	20–100 kHz	7.13 × 10⁻³	1.42	3.02
3C30	100–200 kHz	7.13 × 10⁻³	1.42	3.02
3C90	20–200 kHz	3.20 × 10⁻³	1.46	2.75
3C94	20–200 kHz	2.37 × 10⁻³	1.46	2.75
3C94	200–400 kHz	2.00 × 10⁻⁹	2.60	2.75
3F3	100–300 kHz	2.50 × 10⁻⁴	1.63	2.45
3F3	300–500 kHz	2.00 × 10⁻⁵	1.80	2.50
3F3	500–1000 kHz	3.60 × 10⁻⁹	2.40	2.25
3F4	500–1000 kHz	1.20 × 10⁻³	1.75	2.90
3F4	1000–3000 kHz	1.10 × 10⁻¹¹	2.80	2.40

A curve fit with units, not a law of nature

Charles Steinmetz noticed in 1892 that magnetic loss per cycle rose as a power of the flux density, and the equation named after him is still how ferrite loss is described a century and a bit later. It has no derivation. It is a straight line fitted to log-log measured data, so its three constants carry the units of the axes the fit was drawn on and are valid only over the range that was measured.

The units are the trap. Manufacturers quote k in at least three conventions: mW/cm³ with f in hertz and B in tesla (Ferroxcube’s application notes), mW/cm³ with f in kilohertz and B in tesla (Magnetics’ design guides), and W/m³ with f in hertz and B in tesla (most of the academic literature). The exponents α and β are pure numbers and do not change, but k changes by 1000^α for every step in the frequency unit and 1000^β for every step in the flux unit — at the defaults here that is a factor of about 163.4 G between the two extremes. Two things help. First, 1 mW/cm³ is exactly 1 kW/m³, so that pair never needs converting. Second, always sanity-check the answer against a point the data sheet states: a power ferrite at 100 kHz and 100 mT loses of the order of 50 to 150 mW/cm³ at 100 °C, so an answer of 0.1 or of 100,000 is a unit error, not a discovery.

Sinusoidal only. The equation is written for B = B̂·sin(ωt). A converter does not do that: it applies a square voltage, so the flux is a triangle and dB/dt is constant in each half. Venkatachalam, Sullivan, Abdallah and Tacca’s improved generalised Steinmetz equation (COMPEL 2002) handles that by integrating k_i·|dB/dt|^α·(ΔB)^β−α over the waveform, with k_i chosen so that the result collapses back to Steinmetz for a sinusoid. For the ordinary two-segment triangle that integral has a closed form, and this page evaluates it: at 50% duty the triangle loses a few per cent less than a sinusoid of the same peak, and away from 50% it loses more, because one of the two ramps has been made steeper. What is NOT implemented here is the rest of the iGSE — the recursive splitting of a complicated waveform into major and minor loops. If your flux waveform has minor loops in it, this page will under-read.

Temperature cuts both ways. Loss makes heat, heat changes the loss, and for most power ferrites the loss has a minimum somewhere near 80–100 °C, so a core running below that gets better as it warms and one running above it gets worse. The two empirical rise models offered here are both widely used and they disagree — at the defaults by more than ten degrees — because both are fits to natural convection from a shape neither of them knows. Treat either as an order of magnitude and measure the real thing with a thermocouple in the winding.

For picking the core and the turns in the first place see the SMPS transformer calculator and the gapped core inductance calculator; for the winding’s AC resistance, which is the other half of the loss and the half this page takes as given, the litz wire calculator; and for getting the heat out, the heatsink thermal resistance calculator.

Frequently asked questions

What units are the Steinmetz constants k, alpha and beta in?

Whatever units the curve fit was drawn in — that is the whole problem. α and β are dimensionless, but k absorbs the units of frequency, flux density and loss density. The three common conventions are mW/cm³ with f in Hz and B in T, mW/cm³ with f in kHz and B in T, and W/m³ with f in Hz and B in T. This page asks you which, and prints k restated in all of them.

Is 1 mW/cm³ the same as 1 kW/m³?

Yes, exactly. A cubic metre is 10⁶ cubic centimetres and a kilowatt is 10⁶ milliwatts, so the two cancel. Data sheets use both and a reader who spots that never has to convert between them.

Why does my calculated core loss disagree with the data sheet?

Usually because the constants came from somewhere other than that data sheet. Ferroxcube’s planar application note gives 3C90 constants that over-predict the 3C90 material specification’s own loss figures by 26 to 70% — both documents are genuine, they were just fitted against different measurements over different ranges. Fit your own from the two or three loss figures nearest your operating point.

Can I use the Steinmetz equation for a square-wave converter?

Not directly. It is defined for a sinusoid. Use the iGSE, which this page evaluates in closed form for the triangular flux a square voltage produces. At 50% duty the answer is within a few per cent of the sinusoidal one, so the classic equation is not a disaster there; at 20% or 80% duty it is out by closer to ten per cent, and the error is always in the optimistic direction.

Is peak flux density the same as the flux swing?

No, and it is a factor of 2^β — about a factor of 5.6 at β = 2.5. B̂ is the amplitude: half the peak-to-peak swing. In a forward or push-pull converter the flux swings symmetrically about zero and B̂ is genuinely the peak; in a flyback it swings between two positive values and the Steinmetz equation wants half the SWING, not the peak, with the iGSE handling the rest.

How accurate is the temperature-rise estimate?

It is an order of magnitude, not a design figure. The two empirical models offered here are both in common use and disagree by tens of per cent at the same dissipation, because both are fits to natural convection from a wound assembly whose shape and mounting they know nothing about. Use them to decide whether you are in trouble; use a thermocouple to decide whether you are not.

Related calculators

References

Ferroxcube, 3C90 Material Specification. The three loss figures this page’s default constants are fitted to — at 100 °C: ≤80 kW/m³ at 25 kHz and 200 mT, ≤80 kW/m³ at 100 kHz and 100 mT, and ≈450 kW/m³ at 100 kHz and 200 mT — together with µᵢ 2300 ±20%, B 470 mT at 25 °C and 380 mT at 100 °C, T_C ≥ 220 °C and a density of 4,800 kg/m³.
Ferroxcube, Design of Planar Power Transformers. The published coefficient table reproduced above: Pcore = Cm·f^x·B^y·(ct₀ − ct₁T + ct₂T²) in mW/cm³ with f in Hz and B in T, with separate rows and frequency bands for 3C30, 3C90, 3C94, 3F3 and 3F4, and a temperature factor that equals 1 at 100 °C.
Venkatachalam K, Sullivan CR, Abdallah T, Tacca H. Accurate prediction of ferrite core loss with nonsinusoidal waveforms using only Steinmetz parameters. IEEE COMPEL 2002. The iGSE: Pv = (1/T)∫kᵢ|dB/dt|^α(ΔB)^(β−α)dt, the expression for kᵢ in terms of k, α and β used here, and the recursive major/minor loop split that this page does not implement.
McLyman C W T. Transformer and Inductor Design Handbook, 4th ed. The surface-area temperature rise Tr = 450·ψ^0.826 with ψ in W/cm², used as the default rise model here.
TDK, SIFERRIT material N87. Quoted in the text as a second grade for comparison: µᵢ 2200 ±25%, Bs 490 mT at 25 °C and 390 mT at 100 °C, and relative core losses of 57, 375, 390 and 215 kW/m³ at 25 kHz/200 mT, 100 kHz/200 mT, 300 kHz/100 mT and 500 kHz/50 mT, all at 100 °C — four points that no single power law fits, which is the point.