Core Loss (Steinmetz)

Pv = K · f^x · B^y

Quick answer

This calculator solves Pv = K × f^x × B^y for Core Loss Density. With Steinmetz K 0.5, Frequency 1 kHz, Peak Flux Density 0.5 T, Frequency Exponent 1.1, Flux Exponent 2.35, the result is 0.1957 kW/m³. It solves in 2 directions, so you can enter the values you have and get the one you need.

Calculator

Core Loss Density (W/m³)
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Formula

Pv = K × f^x × B^y

Description

The Steinmetz equation predicts the volumetric core loss of a magnetic material from the switching frequency and the peak AC flux density, using three material constants K, x, and y fitted to the manufacturer’s loss curves. It captures the strong, nonlinear dependence of hysteresis and eddy losses on both frequency and flux swing, and is the basis for choosing core material and operating point in transformers and inductors.

Variables

  • Pv — Core loss per unit volume (W/m³)
  • K — Steinmetz coefficient (material constant)
  • f — Operating frequency (Hz)
  • B — Peak AC flux density (T)
  • x — Frequency exponent (≈1.1–1.7)
  • y — Flux-density exponent (≈2–3)

Practical Notes

K, x, y are valid only over the frequency/flux range they were fitted to; use the improved Generalised Steinmetz (iGSE) for non-sinusoidal waveforms. Multiply Pv by core volume for total core loss.

Symbols and units

Symbol Meaning Default unit Accepted units
Pv Core Loss Density W/m³ W/m³, kW/m³, mW/cm³
Kc Steinmetz K — —
f Frequency Hz Hz, kHz, MHz, GHz
B Peak Flux Density T G, mT, T
x Frequency Exponent — —
y Flux Exponent — —

Step by step

  1. 1. What you know: Steinmetz K 0.5, Frequency 1 kHz, Peak Flux Density 0.5 T, Frequency Exponent 1.1, Flux Exponent 2.35
  2. 2. The relation: Pv = K × f^x × B^y
  3. 3. Substitute: Kc = 0.5, f = 1 kHz, B = 0.5 T, x = 1.1, y = 2.35
  4. 4. Result: Core Loss Density = 0.1957 kW/m³

Worked examples

Minimum range

Given: Steinmetz K 0.025, Frequency 5 Hz, Peak Flux Density 10 G, Frequency Exponent 0.055, Flux Exponent 0.118

Result: Core Loss Density = 0.01209 W/m³

Low range

Given: Steinmetz K 0.25, Frequency 50 Hz, Peak Flux Density 10 mT, Frequency Exponent 0.55, Flux Exponent 1.18

Result: Core Loss Density = 0.009384 W/m³

Typical

Given: Steinmetz K 0.5, Frequency 1 kHz, Peak Flux Density 0.5 T, Frequency Exponent 1.1, Flux Exponent 2.35

Result: Core Loss Density = 0.1957 kW/m³

High range

Given: Steinmetz K 0.8, Frequency 20 kHz, Peak Flux Density 1.5 T, Frequency Exponent 1.76, Flux Exponent 3.76

Result: Core Loss Density = 136500 kW/m³

Maximum range

Given: Steinmetz K 0.008, Frequency 0.2 kHz, Peak Flux Density 15 mT, Frequency Exponent 0.0176, Flux Exponent 0.0376

Result: Core Loss Density = 0.007499 W/m³

Solving for each variable

Solve for Core Loss Density

Steinmetz K 0.025, Frequency 5 Hz, Peak Flux Density 10 G, Frequency Exponent 0.055, Flux Exponent 0.118 → 0.01209 W/m³

Solve for Steinmetz K

Core Loss Density 100 W/m³, Frequency 5 Hz, Peak Flux Density 10 G, Frequency Exponent 0.055, Flux Exponent 0.118 → 206.8

How Core Loss Density changes with Steinmetz K

Steinmetz K (input) Core Loss Density (result)
0.05 19.57 W/m³
0.125 48.92 W/m³
0.25 97.84 W/m³
0.375 146.8 W/m³
0.5 0.1957 kW/m³
0.75 0.2935 kW/m³
1 0.3914 kW/m³
2 0.7827 kW/m³
3.5 1.37 kW/m³
5 1.957 kW/m³

The same result in other units

Unit Value
W/m³ 195.7
kW/m³ 0.1957
mW/cm³ 0.1957

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Frequently asked questions

How do you calculate Core Loss (Steinmetz)?

Use Pv = K × f^x × B^y. With Steinmetz K 0.5, Frequency 1 kHz, Peak Flux Density 0.5 T, Frequency Exponent 1.1, Flux Exponent 2.35, Core Loss Density works out to 0.1957 kW/m³.

What is the formula for Core Loss (Steinmetz)?

The formula is Pv = K × f^x × B^y. The Steinmetz equation predicts the volumetric core loss of a magnetic material from the switching frequency and the peak AC flux density, using three material constants K, x, and y fitted to the manufacturer’s loss curves.

How do you find Steinmetz K when you know the other values?

Rearrange for Steinmetz K: with Core Loss Density 100 W/m³, Frequency 5 Hz, Peak Flux Density 10 G, Frequency Exponent 0.055, Flux Exponent 0.118, Steinmetz K is 206.8.

What units does Core Loss (Steinmetz) use?

Core Loss Density is shown in W/m³, kW/m³, mW/cm³. Values are held in SI base units internally, so you can mix prefixes without converting by hand.

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