The DC current gain: β = I C /I B . Typical values: 50–300 for small-signal BJTs. It varies with temperature, current, and V CE .

α = I C /I E = β/(β+1). Always slightly less than 1 (typically 0.98–0.998). It represents the fraction of emitter current that reaches the collector.

β depends on temperature (+2%/°C typically), collector current (peaks at mid-range, drops at extremes), and V CE . Never design assuming a specific β — use it as a minimum guarantee.

A p = β² (for common-emitter). In dB: 10 log(β²) = 20 log(β). A β of 100 gives 40 dB power gain.

BJT Gain Calculator

β = I_C/I_B

α = I_C/I_E

α = β/(β+1)

BJT Gain Calculator

β (hFE) Current Gain

I_B Base Current (mA)

I_C (enter to find β, optional)

Enter values

BJT Gain Calculator Results

IC (Collector)
—
A

I_E (Emitter)

—

α (I_C/I_E)

—

β (hFE)

—

I_B

—

Power Gain A_p

—

Figure 1: BJT Gain Calculator — enter values to calculate the result with step-by-step workings.

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Table of Contents

Fundamentals

Understanding BJT Current Gain
α vs β

Worked Examples

β=100, I_B=1 mA
Finding β from Measured Currents

Reference

Frequently Asked Questions
Related Calculators

Understanding BJT Current Gain

The BJT’s current gain (β or hFE) is the ratio of collector current to base current: β = I_C/I_B. It is the transistor’s core amplification parameter — a small base current controls a much larger collector current. Typical values range from 50 to 300 for small-signal BJTs, with some Darlington types reaching 10,000+.

β = I_C / I_B (common-emitter current gain)
α = I_C / I_E = β/(β+1) (common-base current gain)
I_E = I_C + I_B (KCL at the transistor)

The calculator above computes all three currents plus α, β, and power gain in dB. The Transistor Base Resistor Calculator uses β directly to find the base resistor for switching circuits. The Transistor Biasing Calculator designs bias circuits that are independent of β.

α vs β

α is always slightly less than 1 (typically 0.98–0.999). It represents the fraction of emitter current that makes it to the collector — the rest is base current. β = α/(1−α), so a small change in α produces a large change in β. If α goes from 0.990 to 0.995, β doubles from 99 to 199. This is why β varies so widely between devices while α is relatively stable.

Example: β=100, I_B=1 mA

β = 100, I_B = 1 mA

I_C = 100 × 1m = 100 mA

I_E = 100m + 1m = 101 mA

α = 100/101 = 0.990

Power gain = 20 log(100) = 40 dB

Example: Finding β from Measured Currents

Measured: I_C = 15 mA, I_B = 0.05 mA

β = 15 / 0.05 = 300

I_E = 15 + 0.05 = 15.05 mA

α = 15/15.05 = 0.9967

Enter I_C in the optional field and I_B in the base current field — the calculator solves for β. The Emitter Resistor Calculator uses I_C and β to find I_E for the R_E calculation.

Frequently Asked Questions

What is β (hFE)?

DC current gain: I_C/I_B. Typical: 50–300 for small-signal BJTs. Varies with temperature (+2%/°C), collector current (peaks mid-range), and V_CE. Never design assuming a specific β — use it as a minimum guarantee.

What is α?

α = I_C/I_E = β/(β+1). Always < 1 (typically 0.98–0.999). More stable than β across devices. A small α change causes a large β change. The Shockley Diode Calculator models the junction physics that determines α.

Why does β vary so much?

β depends on base width, doping profiles, and recombination rates — all affected by manufacturing tolerances. A 2N2222 datasheet lists β = 100–300: a 3:1 spread. The Op-Amp Gain Calculator shows how op-amps eliminate this variability via feedback.

What is power gain?

For common-emitter: A_p ≈ β², or 20 log(β) dB. β=100 gives 40 dB. The MOSFET Calculator calculates g_m instead — MOSFETs are voltage-controlled, so power gain depends on g_m and load resistance.

How do I measure β?

Apply a known I_B and measure I_C: β = I_C/I_B. Many multimeters have an hFE socket. Or measure both currents with the transistor biased in the active region (not saturated). The 555 Timer Calculator can generate a test signal if you need to measure β at a specific frequency.

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Last updated: March 2026