MOSFET Drain Current and Transconductance Calculator

Find the saturation-region drain current, transconductance, and output resistance of an N-channel MOSFET from the square-law model.

🔌 MOSFET Drain Current and Transconductance Calculator
V
V
A/V²
1/V
V
Drain current (ID)
—
Transconductance (gm)
—
Output resistance (ro)
—
Step-by-step working

🔌 What is the MOSFET Drain Current and Transconductance Calculator?

The MOSFET Drain Current and Transconductance Calculator finds the saturation-region drain current Id, small-signal transconductance gm, and output resistance ro of an N-channel MOSFET using the standard square-law model with channel-length modulation, from its gate-source voltage, threshold voltage, and process parameters.

Analog IC and circuit designers use these values to hand-estimate the DC operating point and small-signal gain of a MOSFET amplifier stage before running full SPICE simulation, size current mirrors and biasing networks, and understand the tradeoff between drain current, transconductance, and output resistance for a given overdrive voltage.

A common point of confusion is applying the saturation formula outside its valid range. The square-law saturation equation only holds when the drain-source voltage Vds is at least as large as the overdrive voltage Vov = Vgs - Vth, if Vds is smaller, the device is actually in the triode region and this calculator flags that case rather than silently reporting an inflated current.

This calculator computes Id, gm, and ro from your inputs, automatically detects cutoff and triode-region conditions, and plots the transfer characteristic Id versus Vgs so you can see where your chosen bias point sits on the curve.

📐 Formula

ID = ½k(VGS−VTH)²(1+λVDS)      gm = kVOV(1+λVDS)
VOV = VGS − VTH (overdrive voltage, must be > 0 for conduction)
k = process transconductance parameter (A/V²), λ = channel-length modulation (1/V)
ro = 1 / (λID) (output resistance, valid saturation only, λ > 0)
Example: VGS=3V, VTH=1V, k=0.004 A/V², λ=0.02/V, VDS=5V → ID≈8.8mA, gm≈8.8mS, ro≈5.682kΩ.

📖 How to Use This Calculator

Steps

1
Enter Vgs and Vth. Type the gate-source voltage and the transistor's threshold voltage.
2
Enter k, lambda, and Vds. Type the process transconductance parameter k, the channel-length modulation parameter lambda, and the drain-source voltage Vds.
3
Read the results. The calculator reports drain current Id, transconductance gm, output resistance ro, and flags cutoff or triode conditions.

💡 Example Calculations

Example 1 — Standard Saturation Operating Point

VGS=3V, VTH=1V, k=0.004 A/V², λ=0.02/V, VDS=5V

1
VOV = 3 − 1 = 2 V
2
ID = 0.5 × 0.004 × 2² × (1 + 0.02×5) = 8.8 mA
3
gm = 0.004 × 2 × 1.1 = 8.8 mS, ro = 1/(0.02×0.0088) = 5.682 kΩ
ID = 8.8 mA, gm = 8.8 mS, ro = 5.682 kΩ
Try this example →

Example 2 — Higher Overdrive Voltage

VGS=4V, VTH=1.5V, k=0.006 A/V², λ=0.015/V, VDS=6V

1
VOV = 4 − 1.5 = 2.5 V
2
ID = 0.5 × 0.006 × 2.5² × (1 + 0.015×6) = 20.4375 mA
3
gm = 0.006 × 2.5 × 1.09 = 16.35 mS, ro = 1/(0.015×0.0204375) = 3.262 kΩ
ID = 20.4375 mA, gm = 16.35 mS, ro = 3.262 kΩ
Try this example →

Example 3 — Low-Current Bias Point

VGS=2.5V, VTH=1V, k=0.002 A/V², λ=0.01/V, VDS=4V

1
VOV = 2.5 − 1 = 1.5 V
2
ID = 0.5 × 0.002 × 1.5² × (1 + 0.01×4) = 2.34 mA
3
gm = 0.002 × 1.5 × 1.04 = 3.12 mS, ro = 1/(0.01×0.00234) = 42.735 kΩ
ID = 2.34 mA, gm = 3.12 mS, ro = 42.735 kΩ
Try this example →

❓ Frequently Asked Questions

What is the square-law MOSFET model?+
The square-law model approximates a MOSFET's saturation-region drain current as proportional to the square of its overdrive voltage: Id = 0.5 x k x (Vgs - Vth)^2 x (1 + lambda x Vds), where k is the process transconductance parameter and lambda accounts for channel-length modulation.
What is transconductance (gm) in a MOSFET?+
Transconductance gm is the derivative of drain current with respect to gate-source voltage, dId/dVgs, describing how much the drain current changes for a small change in gate voltage. It sets the small-signal voltage gain of a common-source amplifier stage (roughly gm x Rd).
What is the overdrive voltage Vov?+
Overdrive voltage Vov = Vgs - Vth is the amount by which the gate-source voltage exceeds the threshold voltage. It directly determines both the drain current (which scales with Vov squared) and the transconductance (which scales linearly with Vov).
What is channel-length modulation and why does it matter?+
Channel-length modulation is a second-order effect where the effective channel length shrinks slightly as Vds increases, causing drain current to rise slightly with Vds even in saturation, rather than staying perfectly flat. It is captured by the lambda parameter and gives the MOSFET a finite output resistance ro = 1/(lambda x Id) instead of an ideal infinite one.
How do I know if the MOSFET is in saturation or the triode region?+
The device is in saturation when Vds is greater than or equal to the overdrive voltage Vov = Vgs - Vth. If Vds is smaller than Vov, the transistor is actually in the triode (linear) region, where a different formula applies, and this calculator flags that case since the saturation formula would overestimate the current there.
What happens if Vgs is below the threshold voltage?+
If Vgs is at or below Vth, the overdrive voltage is zero or negative and the transistor is in cutoff, meaning essentially no drain current flows (ignoring subthreshold leakage), this calculator reports Id = 0 in that case.
What is output resistance ro used for?+
Output resistance ro = 1/(lambda x Id) models the finite slope of the Id-Vds curve in saturation, it is used in small-signal amplifier analysis to determine the maximum achievable gain (gm x ro is the intrinsic gain limit of a single transistor) and to compute the actual output resistance of a current-source or amplifier stage.
Where do I find k and lambda for a real MOSFET?+
These parameters come from the transistor's SPICE model or datasheet characterization data, k (often called Kp or Kn in SPICE, combined with W/L) and lambda are process- and device-specific, unlike Vth they are rarely printed directly on a datasheet front page and usually require checking the SPICE model file.
Does this calculator apply to PMOS transistors?+
The magnitudes and formulas are the same for PMOS with all voltage polarities and current directions reversed (Vgs and Vds negative relative to the source, Vth negative). Enter magnitudes here to get the equivalent PMOS drain current and transconductance magnitudes.
What units does this calculator use?+
Vgs, Vth, and Vds are entered in volts, k in amps per volt squared (A/V²), and lambda in inverse volts (1/V). Drain current Id is reported in milliamps, transconductance gm in millisiemens, and output resistance ro in kilohms.
Tags: Mosfet Drain Current Calculator Transconductance Calculator Mosfet Gm Calculator Square Law Mosfet Model Calculator Channel Length Modulation Calculator Calculator Formula Free Online

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What is the square-law MOSFET model?

The square-law model approximates a MOSFET's saturation-region drain current as proportional to the square of its overdrive voltage: Id = 0.5 x k x (Vgs - Vth)^2 x (1 + lambda x Vds), where k is the process transconductance parameter and lambda accounts for channel-length modulation.

What is transconductance (gm) in a MOSFET?

Transconductance gm is the derivative of drain current with respect to gate-source voltage, dId/dVgs, describing how much the drain current changes for a small change in gate voltage. It sets the small-signal voltage gain of a common-source amplifier stage (roughly gm x Rd).

What is the overdrive voltage Vov?

Overdrive voltage Vov = Vgs - Vth is the amount by which the gate-source voltage exceeds the threshold voltage. It directly determines both the drain current (which scales with Vov squared) and the transconductance (which scales linearly with Vov).

What is channel-length modulation and why does it matter?

Channel-length modulation is a second-order effect where the effective channel length shrinks slightly as Vds increases, causing drain current to rise slightly with Vds even in saturation, rather than staying perfectly flat. It is captured by the lambda parameter and gives the MOSFET a finite output resistance ro = 1/(lambda x Id) instead of an ideal infinite one.

How do I know if the MOSFET is in saturation or the triode region?

The device is in saturation when Vds is greater than or equal to the overdrive voltage Vov = Vgs - Vth. If Vds is smaller than Vov, the transistor is actually in the triode (linear) region, where a different formula applies, and this calculator flags that case since the saturation formula would overestimate the current there.

What happens if Vgs is below the threshold voltage?

If Vgs is at or below Vth, the overdrive voltage is zero or negative and the transistor is in cutoff, meaning essentially no drain current flows (ignoring subthreshold leakage), this calculator reports Id = 0 in that case.

What is output resistance ro used for?

Output resistance ro = 1/(lambda x Id) models the finite slope of the Id-Vds curve in saturation, it is used in small-signal amplifier analysis to determine the maximum achievable gain (gm x ro is the intrinsic gain limit of a single transistor) and to compute the actual output resistance of a current-source or amplifier stage.

Where do I find k and lambda for a real MOSFET?

These parameters come from the transistor's SPICE model or datasheet characterization data, k (often called Kp or Kn in SPICE, combined with W/L) and lambda are process- and device-specific, unlike Vth they are rarely printed directly on a datasheet front page and usually require checking the SPICE model file.

Does this calculator apply to PMOS transistors?

The magnitudes and formulas are the same for PMOS with all voltage polarities and current directions reversed (Vgs and Vds negative relative to the source, Vth negative). Enter magnitudes here to get the equivalent PMOS drain current and transconductance magnitudes.

What units does this calculator use?

Vgs, Vth, and Vds are entered in volts, k in amps per volt squared (A/V²), and lambda in inverse volts (1/V). Drain current Id is reported in milliamps, transconductance gm in millisiemens, and output resistance ro in kilohms.

📌 Quick Tips

💡The process transconductance parameter k (sometimes written as Kn' x W/L, or Kp) combines the process transconductance constant with the transistor's width-to-length ratio, it is often given directly in a datasheet or SPICE model rather than computed from first principles.
💡Transconductance gm is the small-signal gain factor that relates a change in Vgs to a change in Id, it is the single most important MOSFET parameter for hand-calculating the voltage gain of a common-source amplifier stage.
💡Setting lambda (channel-length modulation) to 0 models an ideal MOSFET with infinite output resistance, real short-channel devices have nonzero lambda, giving finite ro and a small dependence of Id on Vds even in saturation.
💡This calculator uses the simple square-law model, which is a good hand-calculation approximation for older, longer-channel processes but becomes less accurate for very short-channel modern MOSFETs, where velocity saturation and other effects dominate.
💡For saturation operation the condition Vds >= Vgs - Vth (Vds >= Vov) must hold, if Vds is smaller than the overdrive voltage, the device is actually in the triode (linear) region and this square-law saturation formula overestimates the current.