Earth’s inner core is a solid sphere of iron and nickel about 1,220 km in radius, while the outer core is a liquid layer of the same metals, roughly 2,260 km thick, plus lighter elements. The solid inner core and liquid outer core together generate Earth’s magnetic field through the geodynamo, where convection in the liquid outer core and the solid inner core’s role in heat transfer create the planet’s protective magnetosphere.
Formula
The calculator above computes the volumes of Earth’s inner and outer core using the standard sphere volume formula. For a sphere with radius r, the volume is V = (4/3)Ï€r³. The inner core is treated as a sphere with radius t (input in km). The outer core is the shell between the inner core radius and the outer core boundary, which is the sum of the inner core radius and the outer core thickness d. Its volume is the difference between the volume of the sphere with radius (t + d) and the volume of the inner core sphere.
Variables:
- t = inner core radius (km), default 1,220 km
- d = outer core thickness (km), default 2,260 km
- V_inner = (4/3)πt³ (km³)
- V_outer = (4/3)Ï€(t+d)³ – (4/3)Ï€t³ (km³)
- Ratio = V_outer / V_inner (dimensionless)
Worked Example
Using the default values: t = 1,220 km and d = 2,260 km.
- Inner core volume: V_inner = (4/3) × π × (1,220)³ = (4/3) × π × 1,815,848,000 ≈ 7.61 × 10� km³ (rounded to 0 decimals: 7,608,000,000 km³).
- Outer core outer radius: t + d = 1,220 + 2,260 = 3,480 km.
- Outer core volume: V_outer = (4/3) × Ï€ × (3,480)³ – V_inner = (4/3) × Ï€ × 42,144,192,000 – 7.61 × 10â�¹ ≈ 1.77 × 10¹¹ – 7.61 × 10â�¹ ≈ 1.69 × 10¹¹ km³ (rounded to 0 decimals: 169,000,000,000 km³).
- Ratio: 169,000,000,000 / 7,608,000,000 ≈ 22.21.
The outer core is about 22 times more voluminous than the inner core, which matches the calculator’s output.
Background: How We Know What’s Down There
Direct observation of Earth’s interior is impossible; the deepest drill hole, the Kola Superdeep Borehole, reached only about 12 km. Instead, scientists use seismic waves from earthquakes. P-waves (compressional) and S-waves (shear) travel through the Earth and are bent, reflected, or absorbed by different layers. The fact that S-waves do not pass through the outer core proves it is liquid, because liquids cannot transmit shear waves. The inner core was discovered in 1936 by Inge Lehmann, who noticed that P-waves that should have been shadowed by the core appeared on seismographs, indicating a solid inner sphere that reflects some waves.
Composition: Iron, Nickel, and Lighter Elements
Both cores are primarily iron (~85%) and nickel (~5%), with about 10% lighter elements such as sulfur, oxygen, silicon, and hydrogen. The inner core is solid, despite temperatures exceeding 5,000°C, because the pressure at that depth is over 3.6 million atmospheres, compressing the metal into a crystalline solid. The outer core is liquid because the pressure is slightly lower, allowing the iron to melt. The exact composition of the lighter elements is still debated, but they are crucial because they lower the melting point and drive convection.
State and Physical Conditions
The inner core is a solid sphere with a radius of about 1,220 km, roughly the size of the Moon. It is surrounded by the liquid outer core, which extends to about 3,480 km from the center. Temperatures range from about 5,000 K at the inner core boundary to about 4,000 K at the outer core boundary. Pressures range from about 136 GPa at the outer core’s top to about 360 GPa at the center. The inner core is not uniform; it may have a distinct inner-inner core with different crystal alignment, and it rotates at a slightly different rate than the rest of the planet, a phenomenon detected through seismic wave travel-time changes.
How the Magnetic Field Is Generated
The Earth’s magnetic field is produced by the geodynamo, a self-sustaining process in the outer core. The liquid iron, being an electrical conductor, moves in complex convection currents driven by heat escaping from the inner core. As the fluid moves, it drags and twists magnetic field lines, creating electric currents, which in turn generate more magnetic field. This is a positive feedback loop: the kinetic energy of the moving fluid is converted into magnetic energy. The solid inner core plays a critical role: it releases latent heat and light elements as it slowly freezes, providing the buoyancy that drives the convection. Without the inner core, the outer core might not convect vigorously enough to sustain a strong field.
Why the Magnetic Field Matters
The magnetic field extends far into space, forming the magnetosphere, which deflects charged particles from the solar wind. This protects the atmosphere from being stripped away and shields life from harmful cosmic radiation. The field also causes auroras near the poles. The strength of the field has varied over geological time, with occasional magnetic reversals where the poles flip. The last reversal was about 780,000 years ago. The field has weakened by about 10% since the 19th century, but this is within normal fluctuation. The geodynamo is not guaranteed to persist; Mars, which has a solid core and no active dynamo, lost most of its atmosphere and surface water, likely because its magnetic field shut down billions of years ago.
Common Misconceptions
One frequent misconception is that the inner core is the hottest part of Earth. Actually, the hottest temperatures are in the outer core, because the inner core is solid and cannot convect; it heats up only by conduction, so it is slightly cooler than the outer core just above it. Another is that the inner core is a solid ball of pure iron; it is an alloy with nickel and lighter elements. Also, the magnetic field is not generated by the solid inner core itself; it is generated by the liquid outer core’s motion. The inner core’s role is indirect—it provides heat and composition gradients that drive the convection.
Frequently Asked Questions
Why is the inner core solid if it’s hotter than the outer core’s melting point?
The inner core is under immense pressure, about 360 GPa at the center, which raises the melting point of iron to over 6,000 K. The actual temperature at the inner core boundary is about 5,000-5,700 K, so the iron is below its melting point at that pressure, making it solid. The outer core, at lower pressure, has a lower melting point, so the same temperature keeps it liquid.
Could the inner core ever melt or the outer core solidify?
As the Earth slowly cools, the inner core grows at a rate of about 1 mm per year, and the outer core gradually solidifies onto it. Over billions of years, the outer core could eventually freeze entirely, which would shut down the geodynamo and the magnetic field. This is what likely happened on Mars, but it will not occur for many billions of years, if ever before the Sun expands.
How do scientists know the inner core rotates faster than the rest of Earth?
By analyzing seismic waves from repeated earthquakes that travel through the inner core, researchers have found that the travel times change over years. This indicates that the inner core’s crystal structure, which affects wave speed, is moving relative to the mantle. The differential rotation is estimated at a few tenths of a degree per year, though recent studies suggest it may be slowing or oscillating.
What would happen if the magnetic field disappeared?
Without the magnetic field, the solar wind would directly strike the upper atmosphere, gradually stripping it away, especially hydrogen and oxygen. This would increase radiation at the surface and could harm life, but it would not cause an immediate catastrophe. The atmosphere would be lost over millions of years, and the climate would change. Auroras would appear at all latitudes, and compasses would be useless, but the biggest long-term threat is atmospheric loss.
Is the inner core made of the same stuff as the outer core?
Yes, both are mostly iron and nickel with lighter elements, but the proportions may differ slightly. The inner core is thought to have fewer light elements because they are excluded as it freezes, which is why the outer core is enriched in them. The exact composition is still uncertain, but the basic similarity is well established.
Related
Formula used
in t | Inner core radius | km | 1220 | 0 | 6371 in d | Outer core thickness | km | 2260 | 0 | 6371 out vol_inner | Inner core volume | km^3 | (4/3)*pi*t^3 | 0 out vol_outer | Outer core volume | km^3 | (4/3)*pi*(t+d)^3 - (4/3)*pi*t^3 | 0 out ratio | Outer/Inner volume ratio | - | vol_outer / vol_inner | 2
Each line is one input (in, sel, list) or one result (out: label, unit, formula, decimals). How the calculators work
Method: the standard formula for this calculation, rounded as each result states. See how the calculators work or report an error.
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