The losses had led IS to step up its attacks on civilian targets in the Middle East and Europe, which were likely to intensify, it said.
Almost 300 people died in an IS suicide bombing in Baghdad last week.
The attack came days after the Iraqi government declared that it had retaken full control of the city of Falluja, just west of the capital.
IHS said that in January 2015, six months after IS declared the creation of a caliphate, the group controlled some 90,800 sq km of Iraq and Syria.
By December, that had shrunk by 12,800 sq km to 78,000 sq km, a net loss of 14%.
Since then, IS had lost a further 9,700 sq km and now controlled 68,300 sq km, which is roughly the size of the Republic of Ireland or the US state of West Virginia, according to IHS.
In Syria, IS has come under pressure from government forces backed by Russia and Iran, and Kurdish-led Syrian Democratic Forces fighters supported by a US-led multinational coalition.
The SDF captured the eastern town of Shaddadi, a major hub for IS, in February and in March the ancient town of Palmyra was retaken by government forces.
In Iraq, troops and allied militiamen are preparing for a long-awaited offensive to retake the northern city of Mosul, IS`s last remaining urban stronghold there.
"As the Islamic State`s caliphate shrinks and it becomes increasingly clear that its governance project is failing, the group is re-prioritising insurgency," said Columb Strack, a senior analyst at IHS.
"As a result, we unfortunately expect an increase in mass casualty attacks and sabotage of economic infrastructure, across Iraq and Syria, and further afield, including Europe."
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