MOSFET Drain Current (Saturation)

Id = K · (Vgs − Vth)²

Quick answer

This calculator solves Id = K × (Vgs − Vth)² (K = ½·µ·Cox·W/L) for Drain Current. With Conduction Parameter 10 mA/V², Gate-Source Voltage 12 V, Threshold Voltage 26.4 V, the result is 2.074 A. It solves in 4 directions, so you can enter the values you have and get the one you need.

Calculator

Drain Current (mA)
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Formula

Id = K × (Vgs − Vth)² (K = ½·µ·Cox·W/L)

Description

In saturation an enhancement MOSFET’s drain current follows a square law in the gate overdrive (Vgs minus threshold). The conduction parameter K bundles the carrier mobility, oxide capacitance, and the width-to-length ratio of the channel. This is the design equation for biasing MOSFET amplifier and current-source stages and for sizing switches.

Variables

  • Id — Drain current (A)
  • K — Conduction parameter ½µCox(W/L) (A/V²)
  • Vgs — Gate-source voltage (V)
  • Vth — Threshold voltage (V)

Practical Notes

Valid only above threshold and in saturation (Vds > Vgs − Vth). Transconductance gm = 2·K·(Vgs − Vth) = 2·√(K·Id), so gm grows with bias current—unlike a BJT’s linear gm.

Symbols and units

Symbol Meaning Default unit Accepted units
Id Drain Current mA pA, nA, µA, mA, A, kA
K Conduction Parameter mA/V² A/V², mA/V², µA/V²
Vgs Gate-Source Voltage V pV, nV, µV, mV, V, kV
Vth Threshold Voltage V pV, nV, µV, mV, V, kV

Step by step

  1. 1. What you know: Conduction Parameter 10 mA/V², Gate-Source Voltage 12 V, Threshold Voltage 26.4 V
  2. 2. The relation: Id = K × (Vgs − Vth)² (K = ½·µ·Cox·W/L)
  3. 3. Substitute: K = 10 mA/V², Vgs = 12 V, Vth = 26.4 V
  4. 4. Result: Drain Current = 2.074 A

Related quantities from the same inputs

  • P = V × I = 24.88 W

Worked examples

Minimum range

Given: Conduction Parameter 100 µA/V², Gate-Source Voltage 0.33 V, Threshold Voltage 0.726 V

Result: Drain Current = 15.68 µA

Low range

Given: Conduction Parameter 1 mA/V², Gate-Source Voltage 3.3 V, Threshold Voltage 7.26 V

Result: Drain Current = 15.68 mA

Typical

Given: Conduction Parameter 10 mA/V², Gate-Source Voltage 12 V, Threshold Voltage 26.4 V

Result: Drain Current = 2.074 A

High range

Given: Conduction Parameter 100 mA/V², Gate-Source Voltage 0.23 kV, Threshold Voltage 0.506 kV

Result: Drain Current = 7.618 kA

Maximum range

Given: Conduction Parameter 1 A/V², Gate-Source Voltage 2.3 kV, Threshold Voltage 5.06 kV

Result: Drain Current = 7618 kA

Solving for each variable

Solve for Drain Current

Conduction Parameter 100 µA/V², Gate-Source Voltage 0.33 V, Threshold Voltage 0.726 V → 15.68 µA

Solve for Conduction Parameter

Drain Current 100 µA, Gate-Source Voltage 0.33 V, Threshold Voltage 0.726 V → 0.6377 mA/V²

Solve for Gate-Source Voltage

Drain Current 100 µA, Conduction Parameter 100 µA/V², Threshold Voltage 0.726 V → 1.726 V

Solve for Threshold Voltage

Drain Current 100 µA, Conduction Parameter 100 µA/V², Gate-Source Voltage 0.33 V → -0.67 V

How Drain Current changes with Conduction Parameter

Conduction Parameter (input) Drain Current (result)
1 mA/V² 0.2074 A
2.5 mA/V² 0.5184 A
5 mA/V² 1.037 A
7.5 mA/V² 1.555 A
10 mA/V² 2.074 A
15 mA/V² 3.11 A
20 mA/V² 4.147 A
40 mA/V² 8.294 A
70 mA/V² 14.52 A
100 mA/V² 20.74 A

The same result in other units

Unit Value
µA 2074000
mA 2074
A 2.074
kA 0.002074

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Frequently asked questions

How do you calculate MOSFET Drain Current (Saturation)?

Use Id = K × (Vgs − Vth)² (K = ½·µ·Cox·W/L). With Conduction Parameter 10 mA/V², Gate-Source Voltage 12 V, Threshold Voltage 26.4 V, Drain Current works out to 2.074 A.

What is the formula for MOSFET Drain Current (Saturation)?

The formula is Id = K × (Vgs − Vth)² (K = ½·µ·Cox·W/L). In saturation an enhancement MOSFET’s drain current follows a square law in the gate overdrive (Vgs minus threshold).

How do you find Conduction Parameter when you know the other values?

Rearrange for Conduction Parameter: with Drain Current 100 µA, Gate-Source Voltage 0.33 V, Threshold Voltage 0.726 V, Conduction Parameter is 0.6377 mA/V².

How do you find Gate-Source Voltage when you know the other values?

Rearrange for Gate-Source Voltage: with Drain Current 100 µA, Conduction Parameter 100 µA/V², Threshold Voltage 0.726 V, Gate-Source Voltage is 1.726 V.

What units does MOSFET Drain Current (Saturation) use?

Drain Current is shown in µA, mA, A, kA. Values are held in SI base units internally, so you can mix prefixes without converting by hand.

Related Concepts

All Discrete Amplifiers formulas →
Thermal Voltage Small-Signal Emitter Resistance Transistor Transconductance Diode Dynamic Resistance Common-Emitter Voltage Gain BJT Alpha–Beta Relationship Darlington Pair Current Gain Emitter-Follower Input Impedance

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