MOSFET Threshold Voltage Calculator

Q: What is MOSFET threshold voltage and why does it matter?

The threshold voltage (Vth or Vgs(th)) is the minimum gate-to-source voltage at which the MOSFET begins to conduct. Below Vth, the device is in cutoff and Id = 0. Above Vth, current flows. In switching circuits, the gate driver voltage must significantly exceed Vth to turn the device on fully and minimise on-resistance. Typical N-channel enhancement MOSFETs have Vth between 1 and 5 V.

Q: What is the square-law drain current formula for a MOSFET?

In the saturation region (Vds >= Vgs minus Vth): Id = (Kp / 2) times (Vgs minus Vth) squared. In the linear (triode) region (Vds < Vgs minus Vth): Id = Kp times [(Vgs minus Vth) times Vds minus Vds squared divided by 2]. Kp = mu_n times Cox times W divided by L. The saturation formula is used for amplifier biasing; the linear formula applies to a MOSFET used as a low-resistance switch.

Q: What is the overdrive voltage in a MOSFET?

Overdrive voltage is Vov = Vgs minus Vth. It represents how far above the threshold the gate is driven. In the saturation region, Id = (Kp / 2) times Vov squared. A larger Vov means more current for the same Kp. In switching designs, maximum Vov (full gate drive from a driver IC) is used to minimise Rds_on; in analog amplifiers, Vov is carefully set to control the bias current and transconductance.

Q: How do I find the Kp (process transconductance) of a MOSFET?

Kp is rarely given directly on a datasheet. You can estimate it by picking two Id versus Vgs points from the transfer characteristic graph: Kp = 2 times Id divided by (Vgs minus Vth) squared. Alternatively, read the SPICE model KP parameter. For a first-order estimate, common N-channel enhancement MOSFETs have effective Kp between 50 mA per volt squared (power MOSFETs with many parallel channels) and 500 mA per volt squared (logic-level types).

Q: What are the three operating regions of a MOSFET?

Cutoff: Vgs Vth and Vds >= Vgs minus Vth, Id depends only on Vgs and is approximately constant with Vds; used for amplification. Linear (triode): Vgs > Vth and Vds < Vgs minus Vth, Id depends on both Vgs and Vds; the MOSFET acts as a voltage-controlled resistor. Switching circuits aim for the linear region to minimise Rds_on when fully on.

Q: How does temperature affect MOSFET threshold voltage?

Threshold voltage decreases by roughly 2 to 4 mV per degree Celsius for silicon MOSFETs. A device with Vth = 3 V at 25 C may have Vth = 2.4 V at 175 C. This means the device turns on at a lower gate voltage when hot. In gate driver designs, ensure the gate voltage reliably exceeds the cold Vth on startup and does not cause unwanted turn-on at high temperature during system off states.

Q: What is the difference between an enhancement-mode and depletion-mode MOSFET?

An enhancement-mode MOSFET (the most common type) is off at Vgs = 0 and requires a positive (for N-channel) or negative (for P-channel) gate voltage above Vth to turn on. A depletion-mode MOSFET is on at Vgs = 0 and requires a gate voltage of the opposite polarity to turn off. Depletion-mode types are used in current-source loads, constant-current diodes, and some RF applications.

Q: How do I calculate drain current in the linear region?

When Vds < Vgs minus Vth (linear or triode region): Id = Kp times [(Vgs minus Vth) times Vds minus Vds squared divided by 2]. For Vgs = 5 V, Vth = 2 V, Kp = 100 mA per volt squared, Vds = 1 V: Id = 100 times [3 times 1 minus 0.5] = 100 times 2.5 = 250 mA. The on-resistance in this region is approximately Rds_on = 1 divided by (Kp times Vov).

Q: What is a logic-level MOSFET?

A logic-level MOSFET has a low threshold voltage (Vth typically 1 to 2 V) and is fully enhanced (minimum Rds_on) at Vgs of 4 to 5 V. This allows direct drive from a 3.3 V or 5 V microcontroller GPIO pin without a dedicated gate driver. Standard power MOSFETs require Vgs of 10 V or more for full enhancement, needing a gate driver IC when controlled by a microcontroller.

Q: How do I find the required Vgs for a target drain current?

Rearrange the saturation formula: Vgs = Vth plus square root of (2 times Id divided by Kp). For a target Id = 450 mA with Vth = 2 V and Kp = 100 mA per volt squared: Vgs = 2 plus sqrt(2 times 0.45 / 0.1) = 2 plus sqrt(9) = 2 plus 3 = 5 V. Use the Find Vgs mode of this calculator to compute this directly.

Find MOSFET drain current in any operating region or calculate the gate voltage needed to achieve a target current. Uses the standard square-law MOSFET model.

Gate-Source Voltage (Vgs)5.00 V

0 V15 V

Threshold Voltage (Vth)2.00 V

0.5 V10 V

Transconductance (Kp = μ_nC_oxW/L)100 mA/V²

mA/V²

10 mA/V²1000 mA/V²

Drain-Source Voltage (Vds)5.00 V

0 V20 V

Target Drain Current (Id)450 mA

1 mA1000 mA

Threshold Voltage (Vth)2.00 V

0.5 V10 V

Transconductance (Kp = μ_nC_oxW/L)100 mA/V²

mA/V²

10 mA/V²1000 mA/V²

Drain Current (Id)

—

Status / Region

—

Overdrive Voltage (Vov)

—

Min Vds for Saturation

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⚡ What is MOSFET Threshold Voltage?

MOSFET threshold voltage (Vth) is the minimum gate-to-source voltage at which the transistor forms an inversion layer in the channel and begins conducting between drain and source. Below Vth the device is in cutoff and essentially no current flows. Above Vth the channel opens and current scales with the square of the overdrive voltage (Vgs minus Vth). This square-law relationship is the foundation of both analog amplifier biasing and digital switching circuit design.

The threshold voltage appears in three key design calculations. First, in switching power supplies and motor drivers, the gate driver voltage must reliably exceed Vth under all conditions (including cold start and high temperature variation) to turn the MOSFET fully on. Second, in analog amplifiers and current mirrors, the bias voltage is set a specific overdrive above Vth to achieve a target transconductance and drain current. Third, in load-switch and hot-swap controller circuits, Vth determines the minimum control voltage at which current begins to flow and whether resistive turn-on is possible without a charge pump.

A common confusion is between threshold voltage and the gate voltage needed to drive the MOSFET fully on. The threshold is the turn-on point; the fully-on condition requires Vgs well above Vth. Power MOSFETs specify Rds_on at Vgs = 10 V because at Vgs = Vth the device is barely conducting and Rds_on is enormous. Using the threshold voltage as the operating gate voltage in a switching circuit leads to extreme conduction losses and thermal failure.

This calculator uses the standard square-law MOSFET model from Sedra-Smith and Razavi textbooks. The model is accurate for hand calculations and SPICE-level first-order analysis. It does not account for channel-length modulation (lambda), velocity saturation, or body effect, which are second-order corrections needed only for advanced IC design verification.

📐 Formulas

Cutoff (V_GS below V_th): I_D = 0

Saturation (V_GS > V_th and V_DS ≥ V_ov): I_D = (K_P / 2) × (V_GS − V_th)²

Linear (V_GS > V_th and V_DS below V_ov): I_D = K_P × [(V_GS − V_th) × V_DS − V_DS² / 2]

V_th = threshold voltage (V) - minimum Vgs for channel formation

V_ov = V_GS − V_th = overdrive voltage (V)

K_P = μ_n × C_ox × W/L = process transconductance parameter (A/V² or mA/V²)

Reverse (find Vgs): V_GS = V_th + √(2 × I_D / K_P) for saturation

Example: V_gs=5 V, V_th=2 V, K_P=100 mA/V², V_ds=5 V → V_ov=3 V, saturation → I_D = (100/2) × 9 = 450 mA

📖 How to Use This Calculator

Steps

Choose the calculation mode - select Find Drain Current to compute Id given all operating voltages, or Find Required Vgs to determine the gate voltage needed for a specific current in the saturation region.

Enter the threshold voltage Vth - find Vgs(th) on the MOSFET datasheet, typically given at a small test current (often 250 uA or 1 mA). Logic-level devices have Vth of 1 to 2 V; standard power MOSFETs have Vth of 2 to 5 V.

Enter Vgs, Kp, and Vds (Find Drain Current mode) - type the actual gate-source voltage, the process transconductance Kp in mA per volt squared (estimate from the datasheet transfer curve if not listed), and the drain-source voltage. The calculator automatically determines the operating region.

Read and apply the results - check that the operating region matches your intent (saturation for amplifiers, linear for low-resistance switches). The overdrive voltage and minimum Vds for saturation are shown as secondary results for circuit verification.

💡 Example Calculations

Example 1 - N-Channel MOSFET Switch in Saturation (Vgs=5V, Vth=2V)

Vgs = 5 V, Vth = 2 V, Kp = 100 mA/V², Vds = 5 V

Overdrive voltage: Vov = Vgs - Vth = 5 - 2 = 3 V. Since Vov > 0 the device is ON.

Check region: Vds (5V) ≥ Vov (3V) → saturation. Id is independent of Vds in this region.

Drain current: Id = (Kp/2) × Vov² = (100/2) × 9 = 50 × 9 = 450 mA

Result: I_D = 450 mA, Region = Saturation, Vov = 3 V

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Example 2 - MOSFET in Linear Region (Low Vds Switch)

Vgs = 5 V, Vth = 2 V, Kp = 100 mA/V², Vds = 1 V

Overdrive: Vov = 5 - 2 = 3 V. Check region: Vds (1V) is below Vov (3V) → linear (triode) region.

Linear current: Id = Kp × [(Vov × Vds) - Vds²/2] = 100 × [3 × 1 - 0.5] = 100 × 2.5 = 250 mA

On-resistance estimate: Rds_on = Vds / Id = 1 V / 0.25 A = 4 ohms. Lower Kp or higher Vov reduces Rds_on.

Result: I_D = 250 mA, Region = Linear (Triode)

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Example 3 - Logic-Level MOSFET at 3.3 V Drive (Vth=1.5V)

Vgs = 3.3 V, Vth = 1.5 V, Kp = 200 mA/V², Vds = 5 V

Overdrive: Vov = 3.3 - 1.5 = 1.8 V. Check region: Vds (5V) ≥ Vov (1.8V) → saturation.

Drain current: Id = (200/2) × 1.8² = 100 × 3.24 = 324 mA. This MOSFET is suitable for a 3.3 V logic output gate driver.

Transconductance: gm = Kp × Vov = 200 × 1.8 = 360 mA/V, useful for amplifier voltage gain calculations.

Result: I_D = 324 mA, Vov = 1.8 V, Saturation

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Example 4 - Find Vgs for 100 mA (Find Required Vgs Mode)

Target Id = 100 mA, Vth = 1.5 V, Kp = 50 mA/V²

Use saturation formula rearranged: Vgs = Vth + sqrt(2 × Id / Kp)

Substitute: Vgs = 1.5 + sqrt(2 × 0.1 / 0.05) = 1.5 + sqrt(4) = 1.5 + 2 = 3.5 V

Vds must be at least Vov = 2 V to stay in saturation. Gate driver must supply at least 3.5 V reliably.

Result: Required V_gs = 3.500 V, Vov = 2.000 V

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❓ Frequently Asked Questions

What is MOSFET threshold voltage and why does it matter?+

The threshold voltage (Vth) is the minimum gate-to-source voltage at which the MOSFET begins to conduct. Below Vth the device is in cutoff and Id = 0. Above Vth current flows. In switching circuits the gate driver voltage must significantly exceed Vth to turn the device on fully and minimise on-resistance. Typical N-channel enhancement MOSFETs have Vth between 1 and 5 V. Datasheets list it as Vgs(th) at a specified test drain current.

What is the square-law drain current formula for a MOSFET?+

In saturation (Vds >= Vov): Id = (Kp / 2) times (Vgs - Vth) squared. In the linear region (Vds < Vov): Id = Kp times [(Vgs - Vth) times Vds - Vds squared divided by 2]. Kp = mu_n times Cox times W/L. The saturation formula applies to amplifier biasing; the linear formula applies when the MOSFET is used as a low-resistance switch with a small Vds.

What is overdrive voltage and how does it affect drain current?+

Overdrive voltage is Vov = Vgs - Vth. In saturation, Id = (Kp / 2) times Vov squared. Because drain current scales with Vov squared, small changes in gate voltage produce large changes in current near threshold. At Vov = 3 V and Kp = 100 mA per volt squared: Id = 450 mA. At Vov = 2 V (same Kp): Id = 200 mA. In switching designs, maximise Vov (use a gate driver with adequate output voltage) to minimise Rds_on and conduction losses.

What are the three operating regions of a MOSFET?+

Cutoff: Vgs less than Vth, Id = 0, device is off. Saturation: Vgs greater than Vth and Vds greater than or equal to Vov, Id depends only on Vgs and is nearly constant with Vds. This region is used for amplification and current sourcing. Linear (triode): Vgs greater than Vth and Vds less than Vov, Id depends on both Vgs and Vds. The device acts as a small resistance proportional to 1 divided by (Kp times Vov). Switching circuits use the linear region for the fully-on state.

How do I find Kp for my MOSFET?+

Kp is rarely stated directly on datasheets. Estimate it from the transfer characteristic curve: pick two points (Vgs1, Id1) and (Vgs2, Id2) in saturation, then Kp = 2 times Id divided by (Vgs - Vth) squared. Alternatively, read the SPICE model KP parameter. Typical values are 50 to 200 mA per volt squared for power MOSFETs and 100 to 500 mA per volt squared for logic-level MOSFETs. These are effective Kp values that account for the actual device geometry.

What is a logic-level MOSFET?+

A logic-level MOSFET has a low Vth (1 to 2 V) and reaches minimum Rds_on at Vgs of 4 to 5 V, enabling direct drive from a 3.3 V or 5 V microcontroller GPIO pin. Standard power MOSFETs require Vgs of 10 V for full enhancement and need a dedicated gate driver IC. Always check the Rds_on specification at the actual Vgs you plan to use. An Rds_on of 10 milliohms at Vgs = 10 V may be 50 milliohms at Vgs = 4.5 V.

How does temperature affect MOSFET threshold voltage?+

Threshold voltage decreases by about 2 to 4 mV per degree Celsius for silicon MOSFETs. A device with Vth = 3 V at 25 C may have Vth = 2.4 V at 175 C. This is rarely a problem for switching designs (the gate driver voltage far exceeds Vth in both cases), but it can be significant for circuits that use Vth as a precision voltage reference. The positive temperature coefficient of Rds_on (more resistance when hot) is more commonly the limiting factor in power designs.

How do I calculate the required Vgs for a target drain current?+

Rearrange the saturation formula: Vgs = Vth plus square root of (2 times Id divided by Kp). For Id = 100 mA, Vth = 1.5 V, Kp = 50 mA per volt squared: Vgs = 1.5 plus sqrt(2 times 0.1 / 0.05) = 1.5 plus sqrt(4) = 3.5 V. Note that this assumes the device is in saturation, which requires Vds to be at least Vov = Vgs - Vth = 2 V. Use the Find Required Vgs mode of this calculator to compute this directly.

What is transconductance gm and how is it related to Vth?+

Transconductance is gm = dId/dVgs = Kp times Vov = sqrt(2 times Kp times Id). It measures how effectively the gate controls the drain current. Higher gm means more voltage gain in an amplifier stage. At Vov = 1 V and Kp = 100 mA per volt squared: gm = 100 mA per volt. At Vov = 3 V: gm = 300 mA per volt. In analog design, gm is set by choosing the bias current and overdrive voltage to meet a gain or bandwidth target.

What is channel-length modulation in a MOSFET?+

In reality, drain current in saturation increases slightly with Vds: Id = (Kp / 2) times Vov squared times (1 plus lambda times Vds), where lambda is the channel-length modulation coefficient (typically 0.01 to 0.1 per volt for discrete MOSFETs). This makes the device look like a current source with a finite output resistance Ro = 1 divided by (lambda times Id). This calculator uses the ideal model (lambda = 0), which is accurate for most initial design work and educational purposes.

What is the difference between enhancement-mode and depletion-mode MOSFETs?+

An enhancement-mode MOSFET (the most common type) is off at Vgs = 0 and requires a gate voltage above Vth to turn on. A depletion-mode MOSFET has a channel at Vgs = 0 and can be turned off by applying a negative gate voltage. Depletion-mode N-channel MOSFETs have negative Vth (typically -1 to -3 V), meaning they conduct at zero gate bias. They appear in current-source loads, normally-on power switches, and some RF designs. This calculator applies to enhancement-mode devices.

How does W/L ratio affect drain current in a MOSFET?+

Drain current scales proportionally with W/L because Kp = mu_n times Cox times W/L. Doubling W/L doubles Kp and doubles the drain current at the same Vgs and Vds. In IC design, W/L is chosen to set the current-carrying capacity of each transistor. For discrete power MOSFETs, the effective W/L is set in manufacturing; its effect is captured in the overall Kp value that can be extracted from the transfer characteristic.

🔗 Related Calculators

What is MOSFET threshold voltage and why does it matter?

The threshold voltage (Vth or Vgs(th)) is the minimum gate-to-source voltage at which the MOSFET begins to conduct. Below Vth, the device is in cutoff and Id = 0. Above Vth, current flows. In switching circuits, the gate driver voltage must significantly exceed Vth to turn the device on fully and minimise on-resistance. Typical N-channel enhancement MOSFETs have Vth between 1 and 5 V.

What is the square-law drain current formula for a MOSFET?

In the saturation region (Vds >= Vgs minus Vth): Id = (Kp / 2) times (Vgs minus Vth) squared. In the linear (triode) region (Vds < Vgs minus Vth): Id = Kp times [(Vgs minus Vth) times Vds minus Vds squared divided by 2]. Kp = mu_n times Cox times W divided by L. The saturation formula is used for amplifier biasing; the linear formula applies to a MOSFET used as a low-resistance switch.

What is the overdrive voltage in a MOSFET?

Overdrive voltage is Vov = Vgs minus Vth. It represents how far above the threshold the gate is driven. In the saturation region, Id = (Kp / 2) times Vov squared. A larger Vov means more current for the same Kp. In switching designs, maximum Vov (full gate drive from a driver IC) is used to minimise Rds_on; in analog amplifiers, Vov is carefully set to control the bias current and transconductance.

How do I find the Kp (process transconductance) of a MOSFET?

Kp is rarely given directly on a datasheet. You can estimate it by picking two Id versus Vgs points from the transfer characteristic graph: Kp = 2 times Id divided by (Vgs minus Vth) squared. Alternatively, read the SPICE model KP parameter. For a first-order estimate, common N-channel enhancement MOSFETs have effective Kp between 50 mA per volt squared (power MOSFETs with many parallel channels) and 500 mA per volt squared (logic-level types).

What are the three operating regions of a MOSFET?

Cutoff: Vgs < Vth, Id = 0, the device is off. Saturation (active): Vgs > Vth and Vds >= Vgs minus Vth, Id depends only on Vgs and is approximately constant with Vds; used for amplification. Linear (triode): Vgs > Vth and Vds < Vgs minus Vth, Id depends on both Vgs and Vds; the MOSFET acts as a voltage-controlled resistor. Switching circuits aim for the linear region to minimise Rds_on when fully on.

How does temperature affect MOSFET threshold voltage?

Threshold voltage decreases by roughly 2 to 4 mV per degree Celsius for silicon MOSFETs. A device with Vth = 3 V at 25 C may have Vth = 2.4 V at 175 C. This means the device turns on at a lower gate voltage when hot. In gate driver designs, ensure the gate voltage reliably exceeds the cold Vth on startup and does not cause unwanted turn-on at high temperature during system off states.

What is the difference between an enhancement-mode and depletion-mode MOSFET?

An enhancement-mode MOSFET (the most common type) is off at Vgs = 0 and requires a positive (for N-channel) or negative (for P-channel) gate voltage above Vth to turn on. A depletion-mode MOSFET is on at Vgs = 0 and requires a gate voltage of the opposite polarity to turn off. Depletion-mode types are used in current-source loads, constant-current diodes, and some RF applications.

How do I calculate drain current in the linear region?

When Vds < Vgs minus Vth (linear or triode region): Id = Kp times [(Vgs minus Vth) times Vds minus Vds squared divided by 2]. For Vgs = 5 V, Vth = 2 V, Kp = 100 mA per volt squared, Vds = 1 V: Id = 100 times [3 times 1 minus 0.5] = 100 times 2.5 = 250 mA. The on-resistance in this region is approximately Rds_on = 1 divided by (Kp times Vov).

What is a logic-level MOSFET?

A logic-level MOSFET has a low threshold voltage (Vth typically 1 to 2 V) and is fully enhanced (minimum Rds_on) at Vgs of 4 to 5 V. This allows direct drive from a 3.3 V or 5 V microcontroller GPIO pin without a dedicated gate driver. Standard power MOSFETs require Vgs of 10 V or more for full enhancement, needing a gate driver IC when controlled by a microcontroller.

How do I find the required Vgs for a target drain current?

Rearrange the saturation formula: Vgs = Vth plus square root of (2 times Id divided by Kp). For a target Id = 450 mA with Vth = 2 V and Kp = 100 mA per volt squared: Vgs = 2 plus sqrt(2 times 0.45 / 0.1) = 2 plus sqrt(9) = 2 plus 3 = 5 V. Use the Find Vgs mode of this calculator to compute this directly.

What is the channel-length modulation effect on drain current?

In reality, drain current in the saturation region increases slightly with Vds due to channel-length modulation: Id = (Kp / 2) times Vov squared times (1 plus lambda times Vds), where lambda is the channel-length modulation parameter (typically 0.01 to 0.1 per volt for discrete MOSFETs). This calculator uses the ideal model (lambda = 0), which is accurate enough for most hand calculations and initial design work.

How does W/L ratio affect MOSFET drain current?

Drain current scales directly with W/L because Kp = mu_n times Cox times W/L. Doubling W/L doubles Kp and doubles the drain current at the same Vgs. IC designers adjust W/L to set the current-carrying capacity of each transistor. For discrete MOSFETs, W/L is fixed in manufacturing but an equivalent effective Kp can be estimated from the datasheet transfer curve.

What is the transconductance gm of a MOSFET and how is it calculated?

Transconductance gm is the rate of change of drain current with gate voltage at a fixed Vds: gm = delta Id / delta Vgs = Kp times (Vgs minus Vth) = Kp times Vov = sqrt(2 times Kp times Id). For Kp = 100 mA per volt squared and Vov = 3 V: gm = 100 times 3 = 300 mA per volt. Higher gm means more gain per unit gate voltage swing in amplifier circuits.

📌 Quick Tips

💡The threshold voltage Vth varies with temperature: for silicon MOSFETs it decreases by roughly 2 to 4 mV per degree Celsius increase. Account for this in high-temperature designs.

💡Logic-level MOSFETs have Vth between 1 and 2 V so they turn on fully from a 3.3 V or 5 V microcontroller GPIO pin. Standard MOSFETs require 4 to 6 V Vgs and need a dedicated gate driver.

💡In the saturation region the drain current is independent of Vds, making the MOSFET behave like a current source controlled by Vgs. This is the amplifier bias point.

💡Kp (the process transconductance parameter) equals mu_n times Cox times W divided by L. Datasheets rarely list Kp directly; extract it from the Id versus Vgs transfer curve or from SPICE model parameters.

💡For switching applications, the gate charge Qg and Rds_on are more important than Vth. Use Vth as a first check that the gate driver voltage is sufficient, then move on to Rds_on for conduction loss calculation.