How to use this calculator
Start with a reference field and a reference distance, then tell the calculator where in the heliosphere you want the estimate.
From there, supply the solar-wind speed and the solar rotation period.
The page then combines geometric dilution of the radial field with rotational winding to compute the field components and the resulting spiral angle.
If you have never used a Parker spiral model before, the most important thing to remember is that the magnetic field does not simply weaken with distance; it also changes direction because the rotating Sun keeps twisting the field as the plasma moves outward.
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Enter a reference magnetic field B0 (in nT) at a reference radius r0 (in AU). A common choice is B0 ≈ 5 nT at r0 = 1 AU for typical near-Earth conditions.
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Enter the target distance r (AU) where you want the field estimate.
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Enter the solar-wind speed vsw (km/s). Typical values are ~300–800 km/s.
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Enter the solar rotation period P (days). A commonly used synodic value is ~27 days.
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Click Compute Field. The results table will appear below, and you can use Copy Result to copy a plain-text summary.
Units matter: this page assumes nT for magnetic field, AU for distance, km/s for solar-wind speed, and days for rotation period.
Internally, the calculator converts AU to meters and days to seconds.
If you ever see a result that looks wildly wrong, the culprit is usually a unit mix-up rather than the Parker spiral formula itself.
The Parker spiral in heliocentric spherical coordinates (r, φ) is commonly written as:
Formula: B_r = B_0 r_0/r^2 B_φ = - B_0 r_0/r^2 (Ω r) / v_sw
The rotation rate is computed from the period:
(with P in seconds). The total magnitude and spiral angle are:
and
(this calculator reports ψ in degrees).
Sign convention: the negative sign in Bφ reflects the usual Parker spiral direction for an outward-pointing field in the northern hemisphere.
The calculator uses the absolute values of Br and Bφ when computing ψ so the angle is reported as a positive pitch angle.
In plain language, ψ tells you how “wrapped” the field is: small ψ means nearly radial, while large ψ means the field is trailing strongly around the Sun.
Assumptions used by this page: steady solar wind (no time dependence), purely radial outflow speed vsw, a single rotation rate Ω, and a simple 1/r² falloff for the radial component.
The model is best interpreted as a large-scale average field rather than a minute-by-minute prediction.
Worked example
Suppose you choose a reference field of B0 = 5 nT at r0 = 1 AU, with a slow solar wind of vsw = 400 km/s and a rotation period of P = 27 days.
At r = 1 AU, the model gives Br ≈ 5 nT and an azimuthal component of a few nT in magnitude, producing a spiral angle on the order of a few tens of degrees.
If you increase the distance to several AU while keeping the same reference B0, Br decreases as 1/r², while the ratio |Bφ|/|Br| grows roughly like r (because of the Ωr/v term), so the field becomes increasingly azimuthal.
That trend is the core intuition behind the Parker spiral. Close to the Sun, the field has not had much time to wind up, so the radial part dominates.
Farther out, the outward-moving plasma carries the field line while the Sun keeps rotating underneath it, and the line trails more strongly behind.
The illustrative table below shows one typical set of values. Treat it as a sanity check rather than a universal truth—real solar-wind conditions vary with the solar cycle, heliographic latitude, and transient events.
Illustrative Parker spiral values for B0 = 5 nT at r0 = 1 AU, vsw = 400 km/s, P = 27 days
| r (AU) |
Br (nT) |
Bφ (nT) |
|B| (nT) |
ψ (deg) |
| 0.5 |
20.0 |
-4.7 |
20.6 |
13.3 |
| 1.0 |
5.0 |
-4.7 |
6.9 |
43.5 |
| 5.0 |
0.2 |
-4.7 |
4.7 |
87.6 |
How to interpret the outputs
The results are presented as four quantities. Understanding what each one means helps you decide whether the numbers are reasonable for your use case.
Br is the radial component: it points directly away from (or toward) the Sun and falls off quickly with distance because the same magnetic flux is spread over a larger spherical surface.
Bφ is the azimuthal component: it represents the “wrap” introduced by solar rotation and becomes more important as you go farther out.
The magnitude |B| combines both components and is often what a magnetometer’s total field strength is compared against after coordinate transforms.
Finally, the spiral angle ψ is a compact way to describe geometry: ψ near 0° means nearly radial field lines, while ψ near 90° means the field is almost purely azimuthal.
A useful mental check is to compare the scaling: if you keep B0 fixed at 1 AU and move from 1 AU to 2 AU, Br should drop by a factor of 4.
At the same time, the ratio |Bφ|/|Br| tends to increase with r because the Ωr/v term grows with distance.
That combination is why the outer heliosphere is often described as having a strongly wound spiral field.
The total magnitude does not stay equal to Br; once the azimuthal component becomes important, |B| can remain substantially above the radial component alone.
If you are using the calculator for mission planning or data analysis, it can help to run a small sweep: try a slow wind (e.g., 350–450 km/s) and a fast wind (e.g., 650–800 km/s) at the same distance.
Faster wind reduces the winding because the plasma reaches a given radius in less time, so the Sun has rotated less while the field line segment traveled outward.
In the equations, that shows up as a smaller Ωr/vsw factor and therefore a smaller |Bφ| and smaller ψ.
This is also why magnetic connectivity to the Sun can depend sensitively on the assumed wind speed.
Limitations and interpretation
This calculator is intentionally simple and represents the ideal Parker spiral. It is most useful as a baseline model.
In real data, the heliospheric magnetic field can deviate substantially due to:
- Time variability in solar-wind speed and magnetic polarity (the calculation assumes steady conditions).
- Transient structures such as coronal mass ejections (CMEs), shocks, and magnetic clouds.
- Stream interaction regions and large-scale compressions that change field strength and direction.
- Turbulence and waves that add fluctuations on top of the mean spiral field.
- Latitude/tilt effects and sector structure; the simplest form used here is effectively equatorial and does not model the heliospheric current sheet.
If you need high-fidelity predictions for a specific date/time, consider using measured solar-wind inputs (e.g., from in-situ monitors) and more complete heliospheric models.
For education and quick estimates, the Parker spiral remains a widely used first approximation.
It is the kind of model that earns its value by being simple enough to think with, not by matching every fine-scale fluctuation.
Practical notes (units and sign)
The computation uses r in AU but converts it to meters when evaluating the Ωr/v term (1 AU = 1.496×1011 m).
Br and Bφ are returned in nanotesla (nT). The sign of Bφ follows the standard Parker spiral convention used in many texts.
If you are comparing to a dataset with a different coordinate system or sign convention, you may need to transform components accordingly.
Tip for reproducibility: after you compute a result, use Copy Result and paste the output into your notes or analysis script.
The copied text is formatted as simple key/value lines so it is easy to parse.
If your browser blocks clipboard access, you can still select the results table and copy manually.
When reporting numbers, it is also helpful to state the reference radius and wind speed explicitly, because those two choices strongly affect the interpretation.
FAQ
What should I use for B0 at 1 AU?
A commonly cited near-Earth interplanetary magnetic field magnitude is a few nanotesla.
Using 5 nT at 1 AU is a reasonable starting point for a quiet, typical solar-wind interval.
During disturbed conditions, the field can be significantly larger, and during very quiet periods it can be smaller.
If you have in-situ data for a specific time, using that measured value as B0 will make the comparison more meaningful.
Why does Bφ sometimes look large at big r?
In the ideal Parker model, |Bφ| grows relative to |Br| with distance because the winding term depends on Ωr/vsw.
Even though both components include the same 1/r² factor from the reference scaling, the additional r in Ωr/vsw means the azimuthal-to-radial ratio increases roughly linearly with r.
That is why ψ can approach 90° in the outer heliosphere.
The field is still weakening overall, but its direction is changing in a way that makes the azimuthal part dominate.
Does the calculator include the latitudinal component Bθ?
No. This page computes only the radial and azimuthal components used in the simplest Parker spiral description.
Some extended models include a small Bθ or incorporate current-sheet tilt and latitude dependence.
If you need those effects, treat this calculator as a baseline and consider a more complete heliospheric field model.
Is the rotation period synodic or sidereal?
The input is simply a period in days used to compute Ω = 2π/P.
Many quick calculations use ~27 days (synodic) as a convenient value.
If you prefer a sidereal period or a latitude-dependent rotation rate, enter that value explicitly.
The calculator will apply it consistently.
How can I sanity-check my inputs quickly?
Check that r and r0 are positive and in AU, vsw is in km/s (not m/s), and P is in days.
If you accidentally enter vsw in m/s (e.g., 400000 instead of 400), the computed |Bφ| will be far too small.
If you accidentally enter P in hours instead of days, Ω will be too large and |Bφ| will be too large.
The most common “looks wrong” cases are unit mix-ups.
Accessibility note: after computing, keyboard users can tab to the Copy Result button. Screen readers will announce the updated results because the output region uses aria-live.
