Johnson noise calculator: resistor thermal noise, shot noise and op amp noise

The thermal noise of a resistor as a voltage and a current density, and as an RMS voltage over a bandwidth with the equivalent-noise-bandwidth factor for a first- to fourth-order roll-off, in volts, dBV and as a signal-to-noise ratio: 4.06 nV/√Hz for 1 kΩ at 25 °C. It also gives the shot noise of a DC current, and the total noise of an inverting or non-inverting op amp stage from e_n, i_n and its resistors, with each contributor's share so the one that dominates is plain. The equations are TI's SLVA043; the constants are the exact SI values.

Fig 1 — Thermal noise density √(4kTR) against resistance at 298 K, both axes logarithmic: it rises as the square root of R, half a decade per decade. 1.00 kΩ is marked at 4.06 nV/√Hz.

Noise source

Temperature T (°C)

Bandwidth f_c (−3 dB) (kHz)

Roll-off above f_c

Resistance R (kΩ)

Signal level V_sig (RMS, 0 to skip) (V)

Voltage noise density e_n = √(4kTR): 4.06 nV/√Hz
Current noise density i_n = √(4kT/R): 4.06 pA/√Hz
Absolute temperature T: 298.15 K
Noise bandwidth ENB, brick-wall = f_c: 20.0 kHz
RMS noise voltage e_n·√ENB: 574 nV · −124.8 dBV
RMS noise current i_n·√ENB: 574 pA
Peak to peak, 6 × RMS (99.7 % of the time): 3.44 µV
SNR against V_sig = 1.00 V RMS: 124.8 dB
Available noise power kT·B, into a matched load (derived): −173.9 dBm/Hz · −130.8 dBm over ENB

Brick-wall assumes nothing gets through above 20.0 kHz. If the band is set by a single RC pole, the noise bandwidth is π/2 times wider and the RMS noise √(π/2) = 1.253 times larger: 719 nV.

How this is calculated

Standard: TI SLVA043, Noise Analysis in Operational Amplifier Circuits (Eq 1, 2, 7–17, Table 1); BIPM SI Brochure, 9th edition, §2.2 and §2.3.1; TI SBOA122 Table 1

$e_n = \sqrt{4kTR}, \qquad i_n = \sqrt{\frac{4kT}{R}}, \qquad T = t + 273.15\ \text{K}$: SLVA043 Equation 2, as densities: "e² = ∫4kTR df or i² = ∫(4kT/R) df", a voltage in series with a noiseless resistor or a current in parallel with one. k = 1.380 649 × 10⁻²³ J/K exactly (SI Brochure §2.2; SLVA043 prints 1.38 × 10⁻²³), and t/°C = T/K − 273.15 (SI Brochure §2.3.1).
$i_{sh} = \sqrt{2qI}$: SLVA043 Equation 1, i_n² = ∫2q·i_D df. q = 1.602 176 634 × 10⁻¹⁹ C exactly (SI Brochure §2.2); SLVA043 prints the electron charge as 1.62 × 10⁻¹⁹ C, which is not the SI value, and it is not used.
$e_{on} = e_{in}\sqrt{\frac{1}{2\pi RC}\,\frac{\pi}{2}} \;\Rightarrow\; \text{ENB} = \frac{\pi}{2}\,f_c = 1.57\,f_c; \qquad \text{ENB} = 1.11,\ 1.05,\ 1.025\,f_c \;\text{(orders 2, 3, 4)}$: SLVA043 Equation 11 for one RC pole, and Table 1 for higher orders, as printed. The RMS noise is the density times √ENB. A brick-wall band takes ENB = f_c.
$E_t = \sqrt{e_1^2 + e_2^2 + \dots + e_n^2}$: Independent sources add as powers: SLVA043 Equations 4–6 and the Summary, with its example √(1² + 10²) = 10.05.
$\overline{E^2} = C\left(f_{nc}\ln\frac{f_H}{f_L} + f_H - f_L\right), \qquad f_{nc} = \frac{K^2}{C}, \quad K^2 = \left(e(f)^2 - e_w^2\right) f$: SLVA043 Equation 9, white noise C = e_w² plus 1/f noise with corner f_nc, and the corner from one low-frequency reading (p. 7): the TLV2772's 130 nV/√Hz at 10 Hz on 12 nV/√Hz gives K² = 167560 nV² and f_nc = 1163.6 Hz, printed as 1163 Hz.
$E_{Trms} = \sqrt{\text{ENB}\left(4kTR_2A + 4kTR_3A^2\right) + i_w^2\left(R_2^2 + R_3^2A^2\right)\left(f_{inc}\ln\frac{f_H}{f_L} + \text{ENB}\right) + e_w^2A^2\left(f_{enc}\ln\frac{f_H}{f_L} + \text{ENB}\right)}, \qquad A = \frac{R_1 + R_2}{R_1}$: SLVA043 Equation 17, the inverting or non-inverting stage: R1 from the inverting input to ground (R_g, plus R_s in an inverting stage), R2 the feedback resistor R_f, R3 in series with the non-inverting input (R_s in a non-inverting stage, plus R_b). SLVA043 closes with "f_H/f_L is set equal to ENB"; the calculator takes f_H = ENB. The first term is Equation 12, 4kTR1(R2/R1)² + 4kTR2 + 4kTR3A², simplified. With i_w and R3 removed it is SLVA043's CMOS form.
$E_{iRrms}^2 = \int 4kT\left(\frac{R_1R_2}{R_1 + R_2} + R_3\right)df, \qquad E_{iRrms} = \sqrt{\int 8kTR_3\,df}\;\text{ when } R_3 = R_1 \parallel R_2$: SLVA043 Equations 14 and 15: the resistor noise referred to the input by dividing by the noise gain A_n = (R1 + R2)/R1 (Equation 13). The calculator refers the total the same way, and for an inverting stage also divides by the signal gain R2/R1, to put the noise on the source.
$R = \frac{e_n}{i_n}, \qquad R = \frac{e_n^2}{4kT}, \qquad R = \frac{4kT}{i_n^2}, \qquad R = \frac{2kT}{qI}$: Derived from the equations above, not in SLVA043: the source resistance at which e_n = i_n·R, at which √(4kTR) = e_n, at which √(4kTR) = i_n·R, and at which a current's shot noise equals a resistor's thermal current noise (2qI = 4kT/R, so I·R = 2kT/q).
$E_{pp} \approx 6\,E_{rms} \;(99.7\,\%)$: SLVA043 p. 4: "multiply the rms value by 6 … Erms × 6 = Epp", since thermal and shot noise are Gaussian. The coverage is computed from the Gaussian: 99.73 % for 6, 95.45 % for 4, 99.93 % for 6.8 (SLVA043 prints 99.94 %).
$P_{avail} = kT \cdot \text{ENB}$: Derived: the power the resistor's noise voltage delivers into a matched load R, 4kTR·ENB/(4R). In dBm it is the same for every resistance.

Assumptions

White noise. Resistor noise is thermal only: SLVA043 notes that carbon composition resistors, and others to varying degrees, add flicker ("excess") noise when they carry current, which is not modelled. In op amp mode, 1/f noise is included only through the corner frequencies entered.
The noise bandwidth is set by a low-pass roll-off at f_c from dc: π/2 × f_c for first order (SLVA043's integral), SLVA043 Table 1's factors for orders 2 to 4, or f_c itself for a brick-wall band. SLVA043 does not name the filter response behind Table 1.
Op amp noise is the datasheet's typical e_n and i_n, the same i_n at each input, all sources independent, and an ideal amplifier otherwise, as in SLVA043's model. The resistors' noise is gained to the output at the stage's low-frequency gain across the whole noise bandwidth.
The resistance is its value at the temperature entered; no temperature coefficient is applied. Shot noise is independent of temperature.
Peak-to-peak is 6 × RMS, a Gaussian band that holds 99.7 % of the time, not a hard limit.

What Johnson noise is and what sets it

Every resistor is a noise source. TI's application report SLVA043,Noise Analysis in Operational Amplifier Circuits, opens with J. B. Johnson's 1928 description: "Statistical fluctuation of electric charge exists in all conductors, producing random variation of potential between the ends of the conductor." Its own definition is shorter: "Thermal noise is caused by the thermal agitation of charge carriers (electrons or holes) in a conductor. This noise is present in all passive resistive elements." Two properties make it the floor under every analog design. It is white: "thermal noise is spectrally flat or has a uniform power density". And it does not care what the circuit is doing: it "is independent of current flow". A resistor with nothing connected to it is as noisy as one carrying an amp.

SLVA043's Equation 2 gives the mean-square value as a voltage in series with a noiseless resistor, or as a current in parallel with one: e² = ∫4kTR df and i² = ∫(4kT/R) df. Per root hertz, that is a voltage density of √(4kTR) and a current density of √(4kT/R). The two descriptions are the same resistor; SLVA043's Appendix A works its op amp circuit both ways and gets the same answer. Three things set the number: the resistance, the absolute temperature, and Boltzmann's constant. Nothing else, not the resistor's size, its material or its power rating, enters the equation.

The constants on this page are the exact SI values. The BIPM's SI Brochure fixes them by definition: "the Boltzmann constant, k, is 1.380 649 × 10⁻²³ J/K" and "the elementary charge, e, is 1.602 176 634 × 10⁻¹⁹ C". It also defines the Celsius scale as an offset, t/°C = T/K − 273.15, so the calculator adds 273.15 to the temperature entered. SLVA043 prints k as 1.38 × 10⁻²³, which is the SI value rounded. Worked from the constants, a 1 kΩ resistor at 25 °C, 298.15 K, gives 4 × 1.380 649 × 10⁻²³ × 298.15 × 1000 = 1.6466 × 10⁻¹⁷ V²/Hz, whose square root is 4.06 nV/√Hz. At 300 K the same resistor gives 4.07 nV/√Hz, and at 85 °C 4.45 nV/√Hz: the noise voltage goes as the square root of the absolute temperature, so a 60 °C rise from room temperature adds 9.6 %.

A density is not yet a voltage anyone can measure. SLVA043 is explicit that "the spectral density is integrated over the equivalent noise bandwidth (ENB) of the circuit", and for white noise the integral is the density times the square root of the bandwidth. The 1 kΩ resistor over a 20 kHz band is 4.06 nV/√Hz × √20 000 = 574 nV RMS, or −124.8 dBV: 124.8 dB below a 1 V RMS signal. That is the number the calculator's defaults show.

Johnson noise table: decade resistors at 25 °C

The thermal noise of each decade value from 10 Ω to 10 MΩ at 25 °C, as a voltage density, a current density, and an RMS voltage over a brick-wall 20 kHz band and a brick-wall 1 MHz band. For a band set by a single RC pole at the same −3 dB frequency, multiply the RMS columns by √(π/2) = 1.253; the next section explains why.

R	√(4kTR)	√(4kT/R)	RMS, 20 kHz	dBV, 20 kHz	RMS, 1 MHz
10.0 Ω	406 pV/√Hz	40.6 pA/√Hz	57.4 nV	−144.8	406 nV
100 Ω	1.28 nV/√Hz	12.8 pA/√Hz	181 nV	−134.8	1.28 µV
1.00 kΩ	4.06 nV/√Hz	4.06 pA/√Hz	574 nV	−124.8	4.06 µV
10.0 kΩ	12.8 nV/√Hz	1.28 pA/√Hz	1.81 µV	−114.8	12.8 µV
100 kΩ	40.6 nV/√Hz	0.406 pA/√Hz	5.74 µV	−104.8	40.6 µV
1.00 MΩ	128 nV/√Hz	0.128 pA/√Hz	18.1 µV	−94.8	128 µV
10.0 MΩ	406 nV/√Hz	0.0406 pA/√Hz	57.4 µV	−84.8	406 µV

Two patterns are worth reading off it. The voltage noise rises as the square root of the resistance, so a hundred times the resistance is ten times the noise, and the current noise falls the same way. A 10 kΩ resistor in the audio band is already 1.81 µV RMS, which is why low-noise preamplifiers keep their resistances low. And the bandwidth matters exactly as much as the resistance: fifty times the bandwidth from 20 kHz to 1 MHz is √50 = 7.07 times the noise. The cheapest way to lower the noise in a measurement is usually to stop measuring frequencies that carry no signal. The values are the decades of the E-series; any other value scales by √(R/R_decade).

Noise bandwidth: why the −3 dB frequency is not the bandwidth

A filter's −3 dB frequency is not where its noise stops. Above f_c a real roll-off still passes some noise, and all of it counts. SLVA043 handles this with the equivalent noise bandwidth: the width of the brick-wall filter that would pass the same noise power. Its Equations 10 and 11 integrate a white density through a single RC pole, |A(f)|² = 1/(1 + (2πfRC)²), and get e_on = e_in·√(π/2 × 1/(2πRC)): "So that the ENB = 1.57 x 3dB bandwidth in this first-order system. This result holds for any first-order low-pass function." For steeper filters "the ENB approaches the normal cutoff frequency", and SLVA043's Table 1 gives 1.11, 1.05 and 1.025 × f_c for second to fourth order.

The calculator uses π/2 exactly for a first-order roll-off, since that is SLVA043's own integral, and the table's printed values for the higher orders. SLVA043 does not name the filter response behind the table, so the higher-order factors are best read as typical rather than exact for any particular filter. The effect is not small at first order: the 1 kΩ resistor behind one RC pole at 20 kHz gives 719 nV, not 574 nV, 25 % more. The RC filter calculator finds the pole, and the active filter calculator a second-order one.

Adding noise sources: root-sum-square, not a sum

Two resistors in series do not give twice the noise. SLVA043 works through it with two noise voltages e₁(t) and e₂(t): the square of their sum has a cross term, 2e₁(t)e₂(t), and "Since the noise voltages … arise from separate resistors, they are independent, and the average of their product is zero." What remains is E_t² = e₁² + e₂², and in the report's words "the average mean square value of a sum of separate independent noise sources is the sum of the individual average mean square values." For two resistors that is 4kT(R₁ + R₂): the series resistor makes exactly the noise of a single resistor of the total value, as it should.

The consequence is SLVA043's advice in its Summary: "Because noise adds by the square, when there is an order of magnitude or more difference in value, the lower value can be ignored with very little error." Its example is √(1² + 10²) = 10.05, "If the 1 is ignored, the error is 0.5%", and the moral is "that time will be spent reducing the 10 before working on the 1." That is why the calculator shows each contributor's share of the output noise power in op amp mode: the largest one is the one to work on.

Shot noise and where it overtakes a resistor's noise

A DC current is a stream of discrete charges, and where it crosses a barrier the arrivals are random. SLVA043: "Shot noise results whenever charges cross a potential barrier, like a pn junction. Crossing the potential barrier is a purely random event." Its Equation 1 is i_n² = ∫2q·i_D df: a current density of √(2qI), white like thermal noise, and "Shot noise is independent of temperature." SLVA043 prints the electron charge as 1.62 × 10⁻¹⁹ C; the SI value is 1.602 176 634 × 10⁻¹⁹ C, and the calculator uses that. The printed figure would put shot-noise densities 0.6 % high.

A photodiode current of 10 µA carries 1.79 pA/√Hz of shot noise, 253 pA RMS over 20 kHz. If it flows into a 100 kΩ resistor, as in a transimpedance amplifier, that resistor adds its own √(4kT/R) = 0.406 pA/√Hz. Setting 2qI = 4kT/R gives a derived result that is not in SLVA043 but follows from its two equations: the two are equal when the voltage across the resistor, I·R, is 2kT/q, which is 51.4 mV at 25 °C. With 10 µA in 100 kΩ the DC drop is 1.00 V, well above it, so shot noise is 95 % of the total. Put differently, a larger transimpedance resistor makes the photocurrent's own noise the floor, which is where a receiver wants to be. The transimpedance amplifier calculator sizes that resistor for the signal.

Op amp noise: e_n, i_n and the resistors around it

An op amp datasheet gives its noise referred to the input, as SLVA043 describes: "The part of the internally generated noise that can properly be represented by a voltage source is placed in series with the positive input to an otherwise noiseless op amp. The part of the internally generated noise that can properly be represented by current sources is placed between each input and ground in an otherwise noiseless op amp." So a stage has one voltage noise, e_n, two current noises, i_n at each input, and the thermal noise of every resistor. With the signal sources shorted to ground, SLVA043 notes, "either an inverting or a noninverting op amp circuit, the same circuit results": R1 from the inverting input to ground, R2 from the output back to it, and R3 in series with the non-inverting input.

Each source is then taken alone and carried to the output. R1's noise is gained by R2/R1, R2's appears as it is, and R3's, like e_n, sees the full noise gain A_n = (R1 + R2)/R1. The current noise at the inverting input flows through R2, giving i_n·R2; at the non-inverting input it flows through R3 and is gained by A_n. SLVA043's Equation 17 adds the squares of all six, and, for a CMOS-input part whose current noise is negligible and which needs no R3, reduces to the resistors in the feedback network and e_n alone. Its Equation 14 refers the resistor noise back to the input by dividing by A_n, which gives 4kT·(R1∥R2 + R3), and with R3 = R1∥R2, the usual choice for bias-current cancellation, √(8kT·R3): the compensating resistor doubles the resistor noise power at the input.

The calculator maps the familiar names onto that circuit. R_fis R2 and R_g is R1. A source resistance R_s is part of R3 in a non-inverting stage and part of R1 in an inverting one, and it is reported separately because resistors in series add their noise powers. The defaults in op amp mode are the OPA846 figures from TI's SBOA122, e_n = 1.2 nV/√Hz and i_n = 2.8 pA/√Hz, at a gain of 10 with R_f = 9 kΩ and R_g = 1 kΩ from a 50 Ω source. At the output, the contributions in order are R_g 36.5 nV/√Hz (57 %), i_n·R_f 25.2 nV/√Hz (27 %), R_f 12.2 nV/√Hz (6 %), e_n·A_n 12.0 nV/√Hz (6 %), R_s 9.07 nV/√Hz (4 %). The amplifier's voltage noise, the figure the part is chosen for, is 6 % of the output power: the gain resistor's thermal noise, gained by R_f/R_g = 9, and the current noise through R_f both outweigh it. Scaling the network down tenfold, 900 Ω and 100 Ω, drops the total output noise from 6.85 µV to 2.77 µV over 20 kHz. A low-voltage-noise bipolar amplifier only delivers its e_n in a low-impedance circuit.

The source resistance that makes e_n and i_n equal

For an amplifier fed from a source resistance R, the input noise is √(e_n² + (i_n·R)² + 4kTR): a flat term, one rising a decade per decade of R, and one rising half a decade per decade. The figure in op amp mode draws the three. The voltage and current terms are equal at R = e_n/i_n, and the resistor's own noise overtakes e_n above R = e_n²/4kT and falls below i_n·R above R = 4kT/i_n². These crossings are derived here from SLVA043's model; they are not in the report. For the two amplifiers SBOA122 compares, as followers at 25 °C:

	OPA846 (bipolar)	OPA657 (FET)
e_n, i_n (SBOA122 Table 1)	1.2 nV/√Hz, 2.8 pA/√Hz	4.8 nV/√Hz, 1.3 fA/√Hz
e_n = i_n·R at	429 Ω	3.69 MΩ
√(4kTR) = e_n at	87.5 Ω	1.40 kΩ
√(4kTR) = i_n·R at	2.10 kΩ	9.74 GΩ
Total input noise, 50 Ω source	1.51 nV/√Hz	4.89 nV/√Hz
Total input noise, 1 kΩ source	5.07 nV/√Hz	6.29 nV/√Hz
Total input noise, 10 kΩ source	30.8 nV/√Hz	13.7 nV/√Hz

The bipolar part is the quieter amplifier only for low source resistances. From a 10 kΩ source, whose own noise is 12.8 nV/√Hz, it adds 140 % on top of the source's own noise, while the FET part adds 7 %. The window in which the source resistor is the largest term runs from 87.5 Ω to 2.10 kΩ for the bipolar part, and from 1.40 kΩ to 9.74 GΩ for the FET one. Inside that window the amplifier is doing as well as physics allows.

Worked example: SLVA043's own numbers

SLVA043 works one numeric example, the 1/f corner of the TLV2772, and states a handful of other figures. The calculator's arithmetic is on the left; what the report prints is on the right.

K²        [(130 nV/√Hz)² − (12 nV/√Hz)²] × 10 Hz   = 167560 nV²     SLVA043: 167560 (nV)²
f_nc      167560 nV² / 144 nV²/Hz                  = 1163.6 Hz      SLVA043: 1163 Hz
at f_nc   √2 × 12 nV/√Hz                           = 16.97 nV/√Hz   SLVA043: about 17 nV/√Hz
sum       √(1² + 10²)                              = 10.050         SLVA043: 10.05
error     10.05 / 10 − 1                           = 0.50 %         SLVA043: 0.5%
ENB       (π/2) × f_c, first order                 = 1.5708 × f_c   SLVA043: 1.57 x fc
p-p       6 × rms, within ±3σ                      = 99.73 %        SLVA043: 99.7%
          4 × rms, within ±2σ                      = 95.45 %        SLVA043: 95.4%
          6.8 × rms, within ±3.4σ                  = 99.933 %       SLVA043: 99.94%

Every printed figure is reproduced, with two small differences. The corner frequency, 167560/144, is 1163.61 Hz; SLVA043 prints 1163 Hz, the quotient truncated rather than rounded. And a Gaussian stays within ±3.4σ, a peak-to-peak band of 6.8 × RMS, 99.933 % of the time, where the report prints 99.94%. Neither changes any conclusion. The method for the corner is worth knowing: read the noise at the lowest frequency on the datasheet curve, square it, subtract the square of the white noise, multiply by the frequency, and divide by the white noise squared.

SLVA043 goes no further with the TLV2772, so here it is in a stage: a non-inverting gain of 10, R_f = 9 kΩ and R_g = 1 kΩ, driven from a source of negligible resistance and rolled off by one pole at 10 kHz, from 0.1 Hz. The current noise is left out, as SLVA043's CMOS simplification leaves it out, and the voltage noise corner is the 1163.6 Hz above. This is SLVA043's Equation 17 term by term.

noise gain   A = 1 + 9 kΩ / 1 kΩ                               = 10
ENB          (π/2) × 10 kHz                                   = 15.7 kHz
resistors    ENB × 4kT·R2·A = 15.7 kHz × 1.647e−20 J × 9 kΩ × 10   → 4.82 µV rms at the output
  of which   R_f 0.5 %, R_g 4.7 % of the total power
1/f term     f_enc × ln(ENB / f_L) = 1163.6 Hz × ln(15.7 kHz / 0.1 Hz)   = 13.9 kHz
op amp       e_w·A·√(f_enc·ln(ENB/f_L) + ENB) = 12 nV/√Hz × 10 × √(29.6 kHz)   → 20.7 µV rms
total        E_Trms = √(4.82 µV² + 20.7 µV²)                  = 21.2 µV rms, 127 µV p-p
input        E_Trms / A                                        = 2.12 µV rms

The 1/f term is 47 % of the op amp's own noise power in this band. Leaving it out, as a white-noise-only estimate does, would give 15.8 µV RMS at the output instead of 21.2 µV. SBOA122 states a condition for leaving it out: a bandwidth "greater than 10 times the 1/f noise corner frequency". Here the noise bandwidth is 13.5 times the corner, so that condition is met, and the 1/f term is still close to half the amplifier's noise power. What the rule of thumb does not see is the logarithm: from 0.1 Hz, ln(ENB/f_L) is 12.0, and it multiplies the corner frequency. SBOA122's own context is a dc-coupled, pulse-oriented design, which is not this one. Where the band reaches down to a fraction of a hertz, enter the corner and f_L and let the calculator do the integral.

Where the thermal noise model stops being valid

1/f noise. Thermal and shot noise are white; flicker noise is not. SLVA043: "It is present in all active devices and has various origins. Flicker noise is always associated with a dc current." Its power density goes as 1/f, and its integral, K²·ln(f_H/f_L), grows without limit as the lower frequency falls. The op amp mode includes it through the corner frequencies; the resistor mode does not.

Excess noise in resistors. A resistor carrying current can add flicker noise to its thermal noise. SLVA043: "Flicker noise is also found in carbon composition resistors where it is often referred to as excess noise because it appears in addition to the thermal noise. Other types of resistors also exhibit flicker noise to varying degrees, with wire wound showing the least." The same paragraph gives the way out: "if the current is kept low enough, thermal noise will predominate and the type of resistor used will not change the noise in the circuit." The calculator's resistor figure is the thermal floor; a resistor carrying a large DC current can sit above it.

Burst and avalanche noise. SLVA043 lists five noise sources and sets two aside: "In op amp circuits, burst noise and avalanche noise are normally not problems, or they can be eliminated if present." Avalanche noise "is created when a pn junction is operated in the reverse breakdown mode", and nothing on this page models it.

Peak to peak is a probability. "Thermal noise and shot noise have Gaussian probability density functions." And: "Theoretically the noise amplitude can have values approaching infinity." SLVA043's 6 × RMS is the band the noise stays within 99.7 % of the time, and over a long enough record it will be exceeded. The other sources, it notes, are not Gaussian at all.

The op amp's own figures. SLVA043 calls the datasheet numbers "the typical noise performance of the device": typical, not maximum. They are not one mechanism either: "The voltage and current input referred noise of op amps contains flicker noise, shot noise, and thermal noise." And the model takes i_n at the two inputs as independent sources of equal size, which is how the report draws them. A resistance in the circuit is the one entered, at the temperature entered; the calculator does not apply a resistor's temperature coefficient.

Common Johnson noise mistakes

Adding noise voltages linearly. The contributions in the default op amp stage sum to 13.6 µV at the output if added as numbers; the correct root-sum-square is 6.85 µV. Independent sources add as powers.
Using f_c as the bandwidth. Behind one RC pole the noise bandwidth is π/2 × f_c, and the RMS noise is 25 % higher than the −3 dB frequency suggests.
Putting degrees Celsius into 4kTR. T is absolute: 25 °C is 298.15 K. Entering 25 would understate the noise power by a factor of 11.9, the voltage by 3.45.
Confusing a density with a voltage. 4.06 nV/√Hz is not a voltage until it is multiplied by the square root of a bandwidth; comparing it with a signal in volts, or with an ADC's LSB, is meaningless until then. TheADC noise floor calculator gives the converter's side of that comparison in the same V/√Hz.
Mixing up the two gains of an inverting stage. SLVA043 refers the output noise to the input by dividing by the noise gain, 1 + R_f/R_g, which puts it where e_n sits. The signal only sees R_f/R_g, so for an SNR the output noise has to be divided by that smaller gain instead, which puts it on the source. The calculator shows both.
Choosing a low-e_n amplifier for a high-impedance source. At 10 kΩ the 1.2 nV/√Hz bipolar part above is the noisier of the two. Compare e_n/i_n with the source resistance first.
Forgetting the bias-compensation resistor. R3 = R1∥R2 cancels offset, and, by SLVA043's Equation 15, doubles the resistor noise power referred to the input. For a CMOS part with negligible bias current it buys nothing and costs noise.