diff --git a/.github/actions/spell-check/dictionary/math.txt b/.github/actions/spell-check/dictionary/math.txt
index a533e3d12f..4bad249611 100644
--- a/.github/actions/spell-check/dictionary/math.txt
+++ b/.github/actions/spell-check/dictionary/math.txt
@@ -1,2 +1,3 @@
 powf
 sqrtf
+isnan
diff --git a/.github/actions/spell-check/whitelist/whitelist.txt b/.github/actions/spell-check/whitelist/whitelist.txt
index b7ceec203a..6f102a7b72 100644
--- a/.github/actions/spell-check/whitelist/whitelist.txt
+++ b/.github/actions/spell-check/whitelist/whitelist.txt
@@ -482,6 +482,7 @@ cwchar
 cwctype
 cwd
 cx
+cxcy
 CXFRAME
 CXFULLSCREEN
 CXHSCROLL
diff --git a/src/inc/til.h b/src/inc/til.h
index 5204284a00..e83d2cffe4 100644
--- a/src/inc/til.h
+++ b/src/inc/til.h
@@ -7,6 +7,7 @@
 
 #include "til/at.h"
 #include "til/color.h"
+#include "til/math.h"
 #include "til/some.h"
 #include "til/size.h"
 #include "til/point.h"
diff --git a/src/inc/til/math.h b/src/inc/til/math.h
new file mode 100644
index 0000000000..92afa100c0
--- /dev/null
+++ b/src/inc/til/math.h
@@ -0,0 +1,85 @@
+// Copyright (c) Microsoft Corporation.
+// Licensed under the MIT license.
+
+#pragma once
+
+namespace til
+{
+    // The til::math namespace contains TIL math guidance casts;
+    // they are intended to be used as the first argument to
+    // floating-point universal converters elsewhere in the til namespace.
+    namespace math
+    {
+        namespace details
+        {
+            struct ceiling_t
+            {
+                template<typename O, typename T>
+                static O cast(T val)
+                {
+                    if constexpr (std::is_floating_point_v<T>)
+                    {
+                        THROW_HR_IF(E_ABORT, ::std::isnan(val));
+                        return ::base::saturated_cast<O>(::std::ceil(val));
+                    }
+                    else
+                    {
+                        return ::base::saturated_cast<O>(val);
+                    }
+                }
+            };
+
+            struct flooring_t
+            {
+                template<typename O, typename T>
+                static O cast(T val)
+                {
+                    if constexpr (std::is_floating_point_v<T>)
+                    {
+                        THROW_HR_IF(E_ABORT, ::std::isnan(val));
+                        return ::base::saturated_cast<O>(::std::floor(val));
+                    }
+                    else
+                    {
+                        return ::base::saturated_cast<O>(val);
+                    }
+                }
+            };
+
+            struct rounding_t
+            {
+                template<typename O, typename T>
+                static O cast(T val)
+                {
+                    if constexpr (std::is_floating_point_v<T>)
+                    {
+                        THROW_HR_IF(E_ABORT, ::std::isnan(val));
+                        return ::base::saturated_cast<O>(::std::round(val));
+                    }
+                    else
+                    {
+                        return ::base::saturated_cast<O>(val);
+                    }
+                }
+            };
+
+            struct truncating_t
+            {
+                template<typename O, typename T>
+                static O cast(T val)
+                {
+                    if constexpr (std::is_floating_point_v<T>)
+                    {
+                        THROW_HR_IF(E_ABORT, ::std::isnan(val));
+                    }
+                    return ::base::saturated_cast<O>(val);
+                }
+            };
+        }
+
+        static constexpr details::ceiling_t ceiling; // positives become more positive, negatives become less negative
+        static constexpr details::flooring_t flooring; // positives become less positive, negatives become more negative
+        static constexpr details::rounding_t rounding; // it's rounding, from math class
+        static constexpr details::truncating_t truncating; // drop the decimal point, regardless of how close it is to the next value
+    }
+}
diff --git a/src/inc/til/point.h b/src/inc/til/point.h
index 39a465f073..81691d7b64 100644
--- a/src/inc/til/point.h
+++ b/src/inc/til/point.h
@@ -53,6 +53,22 @@ namespace til // Terminal Implementation Library. Also: "Today I Learned"
         {
         }
 
+        // This template will convert to size from anything that has a X and a Y field that are floating-point;
+        // a math type is required.
+        template<typename TilMath, typename TOther>
+        constexpr point(TilMath, const TOther& other, std::enable_if_t<std::is_floating_point_v<decltype(std::declval<TOther>().X)> && std::is_floating_point_v<decltype(std::declval<TOther>().Y)>, int> /*sentinel*/ = 0) :
+            point(TilMath::template cast<ptrdiff_t>(other.X), TilMath::template cast<ptrdiff_t>(other.Y))
+        {
+        }
+
+        // This template will convert to size from anything that has a x and a y field that are floating-point;
+        // a math type is required.
+        template<typename TilMath, typename TOther>
+        constexpr point(TilMath, const TOther& other, std::enable_if_t<std::is_floating_point_v<decltype(std::declval<TOther>().x)> && std::is_floating_point_v<decltype(std::declval<TOther>().y)>, int> /*sentinel*/ = 0) :
+            point(TilMath::template cast<ptrdiff_t>(other.x), TilMath::template cast<ptrdiff_t>(other.y))
+        {
+        }
+
         constexpr bool operator==(const point& other) const noexcept
         {
             return _x == other._x &&
diff --git a/src/inc/til/size.h b/src/inc/til/size.h
index e551980fbd..67a4102382 100644
--- a/src/inc/til/size.h
+++ b/src/inc/til/size.h
@@ -53,6 +53,30 @@ namespace til // Terminal Implementation Library. Also: "Today I Learned"
         {
         }
 
+        // This template will convert to size from anything that has a X and a Y field that are floating-point;
+        // a math type is required.
+        template<typename TilMath, typename TOther>
+        constexpr size(TilMath, const TOther& other, std::enable_if_t<std::is_floating_point_v<decltype(std::declval<TOther>().X)> && std::is_floating_point_v<decltype(std::declval<TOther>().Y)>, int> /*sentinel*/ = 0) :
+            size(TilMath::template cast<ptrdiff_t>(other.X), TilMath::template cast<ptrdiff_t>(other.Y))
+        {
+        }
+
+        // This template will convert to size from anything that has a cx and a cy field that are floating-point;
+        // a math type is required.
+        template<typename TilMath, typename TOther>
+        constexpr size(TilMath, const TOther& other, std::enable_if_t<std::is_floating_point_v<decltype(std::declval<TOther>().cx)> && std::is_floating_point_v<decltype(std::declval<TOther>().cy)>, int> /*sentinel*/ = 0) :
+            size(TilMath::template cast<ptrdiff_t>(other.cx), TilMath::template cast<ptrdiff_t>(other.cy))
+        {
+        }
+
+        // This template will convert to size from anything that has a Width and a Height field that are floating-point;
+        // a math type is required.
+        template<typename TilMath, typename TOther>
+        constexpr size(TilMath, const TOther& other, std::enable_if_t<std::is_floating_point_v<decltype(std::declval<TOther>().Width)> && std::is_floating_point_v<decltype(std::declval<TOther>().Height)>, int> /*sentinel*/ = 0) :
+            size(TilMath::template cast<ptrdiff_t>(other.Width), TilMath::template cast<ptrdiff_t>(other.Height))
+        {
+        }
+
         constexpr bool operator==(const size& other) const noexcept
         {
             return _width == other._width &&
diff --git a/src/til/ut_til/MathTests.cpp b/src/til/ut_til/MathTests.cpp
new file mode 100644
index 0000000000..056d03edc3
--- /dev/null
+++ b/src/til/ut_til/MathTests.cpp
@@ -0,0 +1,127 @@
+// Copyright (c) Microsoft Corporation.
+// Licensed under the MIT license.
+
+#include "precomp.h"
+
+#include "til/math.h"
+
+using namespace WEX::Common;
+using namespace WEX::Logging;
+using namespace WEX::TestExecution;
+
+class MathTests
+{
+    TEST_CLASS(MathTests);
+
+    template<typename TG, typename TX = ptrdiff_t>
+    struct TestCase
+    {
+        TG given;
+        TX expected;
+    };
+
+    template<class TilMath, typename TG, typename TX, int N>
+    static void _RunCases(TilMath, const std::array<TestCase<TG, TX>, N>& cases)
+    {
+        for (const auto& tc : cases)
+        {
+            VERIFY_ARE_EQUAL(tc.expected, TilMath::template cast<decltype(tc.expected)>(tc.given));
+        }
+    }
+
+    TEST_METHOD(Truncating)
+    {
+        std::array<TestCase<long double, ptrdiff_t>, 8> cases{
+            TestCase<long double, ptrdiff_t>{ 1., 1 },
+            { 1.9, 1 },
+            { -7.1, -7 },
+            { -8.5, -8 },
+            { PTRDIFF_MAX + 0.5, PTRDIFF_MAX },
+            { PTRDIFF_MIN - 0.5, PTRDIFF_MIN },
+            { INFINITY, PTRDIFF_MAX },
+            { -INFINITY, PTRDIFF_MIN },
+        };
+
+        _RunCases(til::math::truncating, cases);
+
+        const auto fn = []() {
+            const auto v = til::math::details::truncating_t::cast<ptrdiff_t>(NAN);
+        };
+        VERIFY_THROWS_SPECIFIC(fn(), wil::ResultException, [](wil::ResultException& e) { return e.GetErrorCode() == E_ABORT; });
+    }
+
+    TEST_METHOD(Ceiling)
+    {
+        std::array<TestCase<long double, ptrdiff_t>, 8> cases{
+            TestCase<long double, ptrdiff_t>{ 1., 1 },
+            { 1.9, 2 },
+            { -7.1, -7 },
+            { -8.5, -8 },
+            { PTRDIFF_MAX + 0.5, PTRDIFF_MAX },
+            { PTRDIFF_MIN - 0.5, PTRDIFF_MIN },
+            { INFINITY, PTRDIFF_MAX },
+            { -INFINITY, PTRDIFF_MIN },
+        };
+
+        _RunCases(til::math::ceiling, cases);
+
+        const auto fn = []() {
+            const auto v = til::math::details::ceiling_t::cast<ptrdiff_t>(NAN);
+        };
+        VERIFY_THROWS_SPECIFIC(fn(), wil::ResultException, [](wil::ResultException& e) { return e.GetErrorCode() == E_ABORT; });
+    }
+
+    TEST_METHOD(Flooring)
+    {
+        std::array<TestCase<long double, ptrdiff_t>, 8> cases{
+            TestCase<long double, ptrdiff_t>{ 1., 1 },
+            { 1.9, 1 },
+            { -7.1, -8 },
+            { -8.5, -9 },
+            { PTRDIFF_MAX + 0.5, PTRDIFF_MAX },
+            { PTRDIFF_MIN - 0.5, PTRDIFF_MIN },
+            { INFINITY, PTRDIFF_MAX },
+            { -INFINITY, PTRDIFF_MIN },
+        };
+
+        _RunCases(til::math::flooring, cases);
+
+        const auto fn = []() {
+            const auto v = til::math::details::flooring_t::cast<ptrdiff_t>(NAN);
+        };
+        VERIFY_THROWS_SPECIFIC(fn(), wil::ResultException, [](wil::ResultException& e) { return e.GetErrorCode() == E_ABORT; });
+    }
+
+    TEST_METHOD(Rounding)
+    {
+        std::array<TestCase<long double, ptrdiff_t>, 8> cases{
+            TestCase<long double, ptrdiff_t>{ 1., 1 },
+            { 1.9, 2 },
+            { -7.1, -7 },
+            { -8.5, -9 },
+            { PTRDIFF_MAX + 0.5, PTRDIFF_MAX },
+            { PTRDIFF_MIN - 0.5, PTRDIFF_MIN },
+            { INFINITY, PTRDIFF_MAX },
+            { -INFINITY, PTRDIFF_MIN },
+        };
+
+        _RunCases(til::math::rounding, cases);
+
+        const auto fn = []() {
+            const auto v = til::math::details::rounding_t::cast<ptrdiff_t>(NAN);
+        };
+        VERIFY_THROWS_SPECIFIC(fn(), wil::ResultException, [](wil::ResultException& e) { return e.GetErrorCode() == E_ABORT; });
+    }
+
+    TEST_METHOD(NormalIntegers)
+    {
+        std::array<TestCase<ptrdiff_t, int>, 4> cases{
+            TestCase<ptrdiff_t, int>{ 1, 1 },
+            { -1, -1 },
+            { PTRDIFF_MAX, INT_MAX },
+            { PTRDIFF_MIN, INT_MIN },
+        };
+
+        _RunCases(til::math::rounding, cases);
+    }
+};
diff --git a/src/til/ut_til/PointTests.cpp b/src/til/ut_til/PointTests.cpp
index bbeba7cd83..8d57e5c32c 100644
--- a/src/til/ut_til/PointTests.cpp
+++ b/src/til/ut_til/PointTests.cpp
@@ -604,4 +604,101 @@ class PointTests
 
         // All ptrdiff_ts fit into a float, so there's no exception tests.
     }
+
+    template<typename T>
+    struct PointTypeWith_xy
+    {
+        T x, y;
+    };
+    template<typename T>
+    struct PointTypeWith_XY
+    {
+        T X, Y;
+    };
+    TEST_METHOD(CastFromFloatWithMathTypes)
+    {
+        PointTypeWith_xy<float> xyFloatIntegral{ 1.f, 2.f };
+        PointTypeWith_xy<float> xyFloat{ 1.6f, 2.4f };
+        PointTypeWith_XY<double> XYDoubleIntegral{ 3., 4. };
+        PointTypeWith_XY<double> XYDouble{ 3.6, 4.4 };
+        Log::Comment(L"0.) Ceiling");
+        {
+            {
+                til::point converted{ til::math::ceiling, xyFloatIntegral };
+                VERIFY_ARE_EQUAL((til::point{ 1, 2 }), converted);
+            }
+            {
+                til::point converted{ til::math::ceiling, xyFloat };
+                VERIFY_ARE_EQUAL((til::point{ 2, 3 }), converted);
+            }
+            {
+                til::point converted{ til::math::ceiling, XYDoubleIntegral };
+                VERIFY_ARE_EQUAL((til::point{ 3, 4 }), converted);
+            }
+            {
+                til::point converted{ til::math::ceiling, XYDouble };
+                VERIFY_ARE_EQUAL((til::point{ 4, 5 }), converted);
+            }
+        }
+
+        Log::Comment(L"1.) Flooring");
+        {
+            {
+                til::point converted{ til::math::flooring, xyFloatIntegral };
+                VERIFY_ARE_EQUAL((til::point{ 1, 2 }), converted);
+            }
+            {
+                til::point converted{ til::math::flooring, xyFloat };
+                VERIFY_ARE_EQUAL((til::point{ 1, 2 }), converted);
+            }
+            {
+                til::point converted{ til::math::flooring, XYDoubleIntegral };
+                VERIFY_ARE_EQUAL((til::point{ 3, 4 }), converted);
+            }
+            {
+                til::point converted{ til::math::flooring, XYDouble };
+                VERIFY_ARE_EQUAL((til::point{ 3, 4 }), converted);
+            }
+        }
+
+        Log::Comment(L"2.) Rounding");
+        {
+            {
+                til::point converted{ til::math::rounding, xyFloatIntegral };
+                VERIFY_ARE_EQUAL((til::point{ 1, 2 }), converted);
+            }
+            {
+                til::point converted{ til::math::rounding, xyFloat };
+                VERIFY_ARE_EQUAL((til::point{ 2, 2 }), converted);
+            }
+            {
+                til::point converted{ til::math::rounding, XYDoubleIntegral };
+                VERIFY_ARE_EQUAL((til::point{ 3, 4 }), converted);
+            }
+            {
+                til::point converted{ til::math::rounding, XYDouble };
+                VERIFY_ARE_EQUAL((til::point{ 4, 4 }), converted);
+            }
+        }
+
+        Log::Comment(L"3.) Truncating");
+        {
+            {
+                til::point converted{ til::math::truncating, xyFloatIntegral };
+                VERIFY_ARE_EQUAL((til::point{ 1, 2 }), converted);
+            }
+            {
+                til::point converted{ til::math::truncating, xyFloat };
+                VERIFY_ARE_EQUAL((til::point{ 1, 2 }), converted);
+            }
+            {
+                til::point converted{ til::math::truncating, XYDoubleIntegral };
+                VERIFY_ARE_EQUAL((til::point{ 3, 4 }), converted);
+            }
+            {
+                til::point converted{ til::math::truncating, XYDouble };
+                VERIFY_ARE_EQUAL((til::point{ 3, 4 }), converted);
+            }
+        }
+    }
 };
diff --git a/src/til/ut_til/SizeTests.cpp b/src/til/ut_til/SizeTests.cpp
index dac72e6eaf..4b708edf37 100644
--- a/src/til/ut_til/SizeTests.cpp
+++ b/src/til/ut_til/SizeTests.cpp
@@ -515,4 +515,140 @@ class SizeTests
 
         // All ptrdiff_ts fit into a float, so there's no exception tests.
     }
+
+    template<typename T>
+    struct SizeTypeWith_XY
+    {
+        T X, Y;
+    };
+    template<typename T>
+    struct SizeTypeWith_cxcy
+    {
+        T cx, cy;
+    };
+    template<typename T>
+    struct SizeTypeWith_WidthHeight
+    {
+        T Width, Height;
+    };
+    TEST_METHOD(CastFromFloatWithMathTypes)
+    {
+        SizeTypeWith_XY<float> XYFloatIntegral{ 1.f, 2.f };
+        SizeTypeWith_XY<float> XYFloat{ 1.6f, 2.4f };
+        SizeTypeWith_cxcy<double> cxcyDoubleIntegral{ 3., 4. };
+        SizeTypeWith_cxcy<double> cxcyDouble{ 3.6, 4.4 };
+        SizeTypeWith_WidthHeight<double> WHDoubleIntegral{ 5., 6. };
+        SizeTypeWith_WidthHeight<double> WHDouble{ 5.6, 6.4 };
+        Log::Comment(L"0.) Ceiling");
+        {
+            {
+                til::size converted{ til::math::ceiling, XYFloatIntegral };
+                VERIFY_ARE_EQUAL((til::size{ 1, 2 }), converted);
+            }
+            {
+                til::size converted{ til::math::ceiling, XYFloat };
+                VERIFY_ARE_EQUAL((til::size{ 2, 3 }), converted);
+            }
+            {
+                til::size converted{ til::math::ceiling, cxcyDoubleIntegral };
+                VERIFY_ARE_EQUAL((til::size{ 3, 4 }), converted);
+            }
+            {
+                til::size converted{ til::math::ceiling, cxcyDouble };
+                VERIFY_ARE_EQUAL((til::size{ 4, 5 }), converted);
+            }
+            {
+                til::size converted{ til::math::ceiling, WHDoubleIntegral };
+                VERIFY_ARE_EQUAL((til::size{ 5, 6 }), converted);
+            }
+            {
+                til::size converted{ til::math::ceiling, WHDouble };
+                VERIFY_ARE_EQUAL((til::size{ 6, 7 }), converted);
+            }
+        }
+
+        Log::Comment(L"1.) Flooring");
+        {
+            {
+                til::size converted{ til::math::flooring, XYFloatIntegral };
+                VERIFY_ARE_EQUAL((til::size{ 1, 2 }), converted);
+            }
+            {
+                til::size converted{ til::math::flooring, XYFloat };
+                VERIFY_ARE_EQUAL((til::size{ 1, 2 }), converted);
+            }
+            {
+                til::size converted{ til::math::flooring, cxcyDoubleIntegral };
+                VERIFY_ARE_EQUAL((til::size{ 3, 4 }), converted);
+            }
+            {
+                til::size converted{ til::math::flooring, cxcyDouble };
+                VERIFY_ARE_EQUAL((til::size{ 3, 4 }), converted);
+            }
+            {
+                til::size converted{ til::math::flooring, WHDoubleIntegral };
+                VERIFY_ARE_EQUAL((til::size{ 5, 6 }), converted);
+            }
+            {
+                til::size converted{ til::math::flooring, WHDouble };
+                VERIFY_ARE_EQUAL((til::size{ 5, 6 }), converted);
+            }
+        }
+
+        Log::Comment(L"2.) Rounding");
+        {
+            {
+                til::size converted{ til::math::rounding, XYFloatIntegral };
+                VERIFY_ARE_EQUAL((til::size{ 1, 2 }), converted);
+            }
+            {
+                til::size converted{ til::math::rounding, XYFloat };
+                VERIFY_ARE_EQUAL((til::size{ 2, 2 }), converted);
+            }
+            {
+                til::size converted{ til::math::rounding, cxcyDoubleIntegral };
+                VERIFY_ARE_EQUAL((til::size{ 3, 4 }), converted);
+            }
+            {
+                til::size converted{ til::math::rounding, cxcyDouble };
+                VERIFY_ARE_EQUAL((til::size{ 4, 4 }), converted);
+            }
+            {
+                til::size converted{ til::math::rounding, WHDoubleIntegral };
+                VERIFY_ARE_EQUAL((til::size{ 5, 6 }), converted);
+            }
+            {
+                til::size converted{ til::math::rounding, WHDouble };
+                VERIFY_ARE_EQUAL((til::size{ 6, 6 }), converted);
+            }
+        }
+
+        Log::Comment(L"3.) Truncating");
+        {
+            {
+                til::size converted{ til::math::truncating, XYFloatIntegral };
+                VERIFY_ARE_EQUAL((til::size{ 1, 2 }), converted);
+            }
+            {
+                til::size converted{ til::math::truncating, XYFloat };
+                VERIFY_ARE_EQUAL((til::size{ 1, 2 }), converted);
+            }
+            {
+                til::size converted{ til::math::truncating, cxcyDoubleIntegral };
+                VERIFY_ARE_EQUAL((til::size{ 3, 4 }), converted);
+            }
+            {
+                til::size converted{ til::math::truncating, cxcyDouble };
+                VERIFY_ARE_EQUAL((til::size{ 3, 4 }), converted);
+            }
+            {
+                til::size converted{ til::math::truncating, WHDoubleIntegral };
+                VERIFY_ARE_EQUAL((til::size{ 5, 6 }), converted);
+            }
+            {
+                til::size converted{ til::math::truncating, WHDouble };
+                VERIFY_ARE_EQUAL((til::size{ 5, 6 }), converted);
+            }
+        }
+    }
 };
diff --git a/src/til/ut_til/sources b/src/til/ut_til/sources
index af602729cd..0fd583bafb 100644
--- a/src/til/ut_til/sources
+++ b/src/til/ut_til/sources
@@ -18,6 +18,7 @@ SOURCES = \
     ColorTests.cpp \
     OperatorTests.cpp \
     PointTests.cpp \
+    MathTests.cpp \
     RectangleTests.cpp \
     SizeTests.cpp \
     SomeTests.cpp \
diff --git a/src/til/ut_til/til.unit.tests.vcxproj b/src/til/ut_til/til.unit.tests.vcxproj
index d2e91bf250..011a39a768 100644
--- a/src/til/ut_til/til.unit.tests.vcxproj
+++ b/src/til/ut_til/til.unit.tests.vcxproj
@@ -13,6 +13,7 @@
     <ClCompile Include="BitmapTests.cpp" />
     <ClCompile Include="OperatorTests.cpp" />
     <ClCompile Include="PointTests.cpp" />
+    <ClCompile Include="MathTests.cpp" />
     <ClCompile Include="RectangleTests.cpp" />
     <ClCompile Include="SizeTests.cpp" />
     <ClCompile Include="ColorTests.cpp" />