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In this article by Spiegel Online (German), there is a claim that humans cannot absorb/digest/use the iron present in spinach:

Das tatsächlich im Spinat enthaltende Eisen ist für Menschen per Verdauung noch nicht einmal verwertbar. Korrekt wäre es nach aktuellem Kenntnisstand, seinem Nachwuchs die Vorzüge des grünen Papps stattdessen mit seinem Vitamin-, Eiweiß- und Mineralgehalt zu begründen.

Free Translation:

The actual iron content in spinach is not even usable by humans through digestion. Based on current knowledge, it would be more correct instead to convince the young to eat the greens based on its vitamin, protein and mineral content.

Can humans digestive system absorb the iron present in spinach?

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There are conflicting studies on this subject.

First of all, dietary iron is usually categorized into one of the two forms 'heme iron' and 'non-heme iron'. Heme iron is technically a ferrous ion bound to an organic molecule, chemically similar or identical to the form iron is usually bound in the human body. This form of iron is only available in products of animal origin, especially red meat. Non-heme iron are much simpler inorganic ferrous or ferric compounds, which are present both in vegetables and in animal products. Even if the actual numbers differ between different publications, it is commonly accepted that the bioavailability (the ratio actually available for digestion) of heme iron is significantly higher than for non-heme iron. In 'The relative dietary importance of haem and non-haem iron' (Bezwoda, Bothwell, Charlton et al.) the bioavailability of heme iron was measured to be about 20%, while the availability of non-heme iron varied between 6% and 18% depending on the amount of iron present in the meal. The relative availability dropped distinctly when the amount of iron increased, meaning that the absolute amount of iron actually absorbed stayed nearly the same, even if the meal itself contained much more iron.

These findings seem to indicate that, at least for the purpose of obtaining iron, it might not be particularly beneficial to eat iron-rich vegetables at all (not just limited to spinach), since the absolute amount of bioavailable non-heme iron is limited.

Another issue particularly valid for spinach is the high content of oxalic acid. It is known that oxalic acid reacts with many minerals, lowering or even inhibiting the bioavailability of the minerals. Oxalic acid reacts particularly easy with calcium to form calcium oxalate, which not only makes the calcium completely unusable for the human body, but is also concidered a poisonous substance and a major contributor to the formation of kidney stones (a kidney stone is basically a large crystal of calcium oxalate). It is however disputed if oxalic acid has a relevant impact on the bioavailability of iron, although it can react with iron to form ferrous oxalate or ferric oxalate.

If we now look into some of the publications on this subject, you can actually find almost the complete range of interpretations.

An often quoted article from 'Scientific American' - 'Iron Deficiency' (Neil S. Scrimshaw):

Although vegetables, particlarly spinach, are regarded as impressive sources of iron, plant (nonheme) iron is relatively poorly absorbed. For instance, only 1.4 percent of the iron from spinach can be taken in by the body; ... In contrast, 20 percent of iron from red meat, in the form of heme iron, can be absorbed.

In the publication 'Oxalic acid does not influence nonhaem iron absorption in humans: a comparison of kale and spinach meals' (Bonsmann, Walczyk, Renggli, Hurrell), the bioavailability of iron from spinach was found to be about 8% and that the precence of oxalic acid does not have significant impact on the availability.

And then we also have 'Oxalate content of food and its effect on humans' (Noonan, Savage), in which the discussion is mainly about the impact on calcium absorbtion, but where they also conclude with a certain insecurity when it comes to iron:

The availability of magnesium, iron, sodium, potassium and phosphorous may also be restricted.

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The answer given by Tor-Einar Jarnbjo is mostly correct, however incomplete.

There is evidence that vitamin C increases non-heme iron resorption [Seshadri et al. (1985)] and that this effect is also seen when co-consuming iron-rich and vitamin C-rich components [shown for guava by Near et. al. (2013)].

Synthesizing the previous answer with my answer, I would conclude that there might be better (vegetable) iron sources than spinach (e.g. legumes), but that spinach indeed is a source for iron in the human diet, especially in combination with vitamin C-rich vegetables or fruits (e.g. oranges, lemons, guava, bell pepper, ...). The extent might be debatable but the Spiegel seems to make a far too strong case.

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