diff --git a/.github/workflows/ci.yaml b/.github/workflows/ci.yaml
index 48a7df79..d3d20fb2 100644
--- a/.github/workflows/ci.yaml
+++ b/.github/workflows/ci.yaml
@@ -106,7 +106,7 @@ jobs:
           cache-dependency-glob: "pyproject.toml"
       - name: Install xarray and dependencies
         run: |
-          uv add --dev .[complete] pint>=0.22
+          uv add --dev ".[complete]" "pint>=0.22"
       - name: Install upstream flox
         run: |
           uv add git+https://github.com/dcherian/flox.git@${{ github.ref }}
diff --git a/flox/aggregations.py b/flox/aggregations.py
index 6246942b..d0ce8343 100644
--- a/flox/aggregations.py
+++ b/flox/aggregations.py
@@ -15,6 +15,8 @@
 from . import aggregate_flox, aggregate_npg, xrutils
 from . import xrdtypes as dtypes
 from .lib import dask_array_type, sparse_array_type
+from .multiarray import MultiArray
+from .xrutils import notnull
 
 if TYPE_CHECKING:
     FuncTuple = tuple[Callable | str, ...]
@@ -161,8 +163,8 @@ def __init__(
         self,
         name: str,
         *,
-        numpy: str | None = None,
-        chunk: str | FuncTuple | None,
+        numpy: partial | str | None = None,
+        chunk: partial | str | FuncTuple | None,
         combine: str | FuncTuple | None,
         preprocess: Callable | None = None,
         finalize: Callable | None = None,
@@ -343,57 +345,183 @@ def _mean_finalize(sum_, count):
 )
 
 
-# TODO: fix this for complex numbers
-def _var_finalize(sumsq, sum_, count, ddof=0):
+def var_chunk(
+    group_idx, array, *, skipna: bool, engine: str, axis=-1, size=None, fill_value=None, dtype=None
+):
+    # Calculate length and sum - important for the adjustment terms to sum squared deviations
+    array_lens = generic_aggregate(
+        group_idx,
+        array,
+        func="nanlen",
+        engine=engine,
+        axis=axis,
+        size=size,
+        fill_value=0,  # Unpack fill value bc it's currently defined for multiarray
+        dtype=dtype,
+    )
+
+    array_sums = generic_aggregate(
+        group_idx,
+        array,
+        func="nansum" if skipna else "sum",
+        engine=engine,
+        axis=axis,
+        size=size,
+        fill_value=0,  # Unpack fill value bc it's currently defined for multiarray
+        dtype=dtype,
+    )
+
+    # Calculate sum squared deviations - the main part of variance sum
     with np.errstate(invalid="ignore", divide="ignore"):
-        result = (sumsq - (sum_**2 / count)) / (count - ddof)
-    result[count <= ddof] = np.nan
-    return result
+        array_means = array_sums / array_lens
+
+    sum_squared_deviations = generic_aggregate(
+        group_idx,
+        (array - array_means[..., group_idx]) ** 2,
+        func="nansum" if skipna else "sum",
+        engine=engine,
+        axis=axis,
+        size=size,
+        fill_value=0,  # Unpack fill value bc it's currently defined for multiarray
+        dtype=dtype,
+    )
+
+    return MultiArray((sum_squared_deviations, array_sums, array_lens))
+
+
+def _var_combine(array, axis, keepdims=True):
+    def clip_last(array, ax, n=1):
+        """Return array except the last element along axis
+        Purely included to tidy up the adj_terms line
+        """
+        assert n > 0, "Clipping nothing off the end isn't implemented"
+        not_last = [slice(None, None) for i in range(array.ndim)]
+        not_last[ax] = slice(None, -n)
+        return array[*not_last]
+
+    def clip_first(array, ax, n=1):
+        """Return array except the first element along axis
+        Purely included to tidy up the adj_terms line
+        """
+        not_first = [slice(None, None) for i in range(array.ndim)]
+        not_first[ax] = slice(n, None)
+        return array[*not_first]
+
+    for ax in axis:
+        if array.shape[ax] == 1:
+            continue
+
+        sum_deviations, sum_X, sum_len = array.arrays
+
+        # Calculate parts needed for cascading combination
+        cumsum_X = np.cumsum(sum_X, axis=ax)
+        cumsum_len = np.cumsum(sum_len, axis=ax)
+
+        # There will be instances in which one or both chunks being merged are empty
+        # In which case, the adjustment term should be zero, but will throw a divide-by-zero error
+        # We're going to add a constant to the bottom of the adjustment term equation on those instances
+        # and count on the zeros on the top making our adjustment term still zero
+        zero_denominator = (clip_last(cumsum_len, ax) == 0) | (clip_first(sum_len, ax) == 0)
+
+        # Adjustment terms to tweak the sum of squared deviations because not every chunk has the same mean
+        with np.errstate(invalid="ignore", divide="ignore"):
+            adj_terms = (
+                clip_last(cumsum_len, ax) * clip_first(sum_X, ax)
+                - clip_first(sum_len, ax) * clip_last(cumsum_X, ax)
+            ) ** 2 / (
+                clip_last(cumsum_len, ax)
+                * clip_first(sum_len, ax)
+                * (clip_last(cumsum_len, ax) + clip_first(sum_len, ax))
+                + zero_denominator.astype(int)
+            )
+
+        check = adj_terms * zero_denominator
+        assert np.all(check[notnull(check)] == 0), (
+            "Instances where we add something to the denominator must come out to zero"
+        )
+
+        array = MultiArray(
+            (
+                np.sum(sum_deviations, axis=ax, keepdims=keepdims)
+                + np.sum(adj_terms, axis=ax, keepdims=keepdims),  # sum of squared deviations
+                np.sum(sum_X, axis=ax, keepdims=keepdims),  # sum of array items
+                np.sum(sum_len, axis=ax, keepdims=keepdims),  # sum of array lengths
+            )
+        )
+    return array
+
+
+def is_var_chunk_reduction(agg: Callable) -> bool:
+    if isinstance(agg, partial):
+        agg = agg.func
+    return agg is blockwise_or_numpy_var or agg is var_chunk
+
+
+def _var_finalize(multiarray, ddof=0):
+    den = multiarray.arrays[2]
+    den -= ddof
+    # preserve nans for groups with 0 obs; so these values are -ddof
+    with np.errstate(invalid="ignore", divide="ignore"):
+        ret = multiarray.arrays[0]
+        ret /= den
+    ret[den < 0] = np.nan
+    return ret
 
 
-def _std_finalize(sumsq, sum_, count, ddof=0):
-    return np.sqrt(_var_finalize(sumsq, sum_, count, ddof))
+def _std_finalize(multiarray, ddof=0):
+    return np.sqrt(_var_finalize(multiarray, ddof))
+
+
+def blockwise_or_numpy_var(*args, skipna: bool, ddof=0, std=False, **kwargs):
+    res = _var_finalize(var_chunk(*args, skipna=skipna, **kwargs), ddof)
+    return np.sqrt(res) if std else res
 
 
 # var, std always promote to float, so we set nan
 var = Aggregation(
     "var",
-    chunk=("sum_of_squares", "sum", "nanlen"),
-    combine=("sum", "sum", "sum"),
+    chunk=partial(var_chunk, skipna=False),
+    numpy=partial(blockwise_or_numpy_var, skipna=False),
+    combine=(_var_combine,),
     finalize=_var_finalize,
-    fill_value=0,
+    fill_value=((0, 0, 0),),
     final_fill_value=np.nan,
-    dtypes=(None, None, np.intp),
+    dtypes=(None,),
     final_dtype=np.floating,
 )
+
 nanvar = Aggregation(
     "nanvar",
-    chunk=("nansum_of_squares", "nansum", "nanlen"),
-    combine=("sum", "sum", "sum"),
+    chunk=partial(var_chunk, skipna=True),
+    numpy=partial(blockwise_or_numpy_var, skipna=True),
+    combine=(_var_combine,),
     finalize=_var_finalize,
-    fill_value=0,
+    fill_value=((0, 0, 0),),
     final_fill_value=np.nan,
-    dtypes=(None, None, np.intp),
+    dtypes=(None,),
     final_dtype=np.floating,
 )
+
 std = Aggregation(
     "std",
-    chunk=("sum_of_squares", "sum", "nanlen"),
-    combine=("sum", "sum", "sum"),
+    chunk=partial(var_chunk, skipna=False),
+    numpy=partial(blockwise_or_numpy_var, skipna=False, std=True),
+    combine=(_var_combine,),
     finalize=_std_finalize,
-    fill_value=0,
+    fill_value=((0, 0, 0),),
     final_fill_value=np.nan,
-    dtypes=(None, None, np.intp),
+    dtypes=(None,),
     final_dtype=np.floating,
 )
 nanstd = Aggregation(
     "nanstd",
-    chunk=("nansum_of_squares", "nansum", "nanlen"),
-    combine=("sum", "sum", "sum"),
+    chunk=partial(var_chunk, skipna=True),
+    numpy=partial(blockwise_or_numpy_var, skipna=True, std=True),
+    combine=(_var_combine,),
     finalize=_std_finalize,
-    fill_value=0,
+    fill_value=((0, 0, 0),),
     final_fill_value=np.nan,
-    dtypes=(None, None, np.intp),
+    dtypes=(None,),
     final_dtype=np.floating,
 )
 
diff --git a/flox/core.py b/flox/core.py
index 3109e85d..8681efed 100644
--- a/flox/core.py
+++ b/flox/core.py
@@ -44,6 +44,7 @@
     _atleast_1d,
     _initialize_aggregation,
     generic_aggregate,
+    is_var_chunk_reduction,
     quantile_new_dims_func,
 )
 from .cache import memoize
@@ -1289,7 +1290,8 @@ def chunk_reduce(
     # optimize that out.
     previous_reduction: T_Func = ""
     for reduction, fv, kw, dt in zip(funcs, fill_values, kwargss, dtypes):
-        if empty:
+        # UGLY! but this is because the `var` breaks our design assumptions
+        if empty and not is_var_chunk_reduction(reduction):
             result = np.full(shape=final_array_shape, fill_value=fv, like=array)
         elif is_nanlen(reduction) and is_nanlen(previous_reduction):
             result = results["intermediates"][-1]
@@ -1298,6 +1300,10 @@ def chunk_reduce(
             kw_func = dict(size=size, dtype=dt, fill_value=fv)
             kw_func.update(kw)
 
+            # UGLY! but this is because the `var` breaks our design assumptions
+            if is_var_chunk_reduction(reduction):
+                kw_func.update(engine=engine)
+
             if callable(reduction):
                 # passing a custom reduction for npg to apply per-group is really slow!
                 # So this `reduction` has to do the groupby-aggregation
@@ -2785,6 +2791,7 @@ def groupby_reduce(
             array = array.view(np.int64)
         elif is_cftime:
             offset = array.min()
+            assert offset is not None
             array = datetime_to_numeric(array, offset, datetime_unit="us")
 
     if nax == 1 and by_.ndim > 1 and expected_ is None:
diff --git a/flox/multiarray.py b/flox/multiarray.py
new file mode 100644
index 00000000..20116099
--- /dev/null
+++ b/flox/multiarray.py
@@ -0,0 +1,97 @@
+from collections.abc import Callable
+from typing import Self
+
+import numpy as np
+
+MULTIARRAY_HANDLED_FUNCTIONS: dict[Callable, Callable] = {}
+
+
+class MultiArray:
+    arrays: tuple[np.ndarray, ...]
+
+    def __init__(self, arrays):
+        self.arrays = arrays
+        assert all(arrays[0].shape == a.shape for a in arrays), "Expect all arrays to have the same shape"
+
+    def astype(self, dt, **kwargs) -> Self:
+        return type(self)(tuple(array.astype(dt, **kwargs) for array in self.arrays))
+
+    def reshape(self, shape, **kwargs) -> Self:
+        return type(self)(tuple(array.reshape(shape, **kwargs) for array in self.arrays))
+
+    def squeeze(self, axis=None) -> Self:
+        return type(self)(tuple(array.squeeze(axis) for array in self.arrays))
+
+    def __setitem__(self, key, value) -> None:
+        assert len(value) == len(self.arrays)
+        for array, val in zip(self.arrays, value):
+            array[key] = val
+
+    def __array_function__(self, func, types, args, kwargs):
+        if func not in MULTIARRAY_HANDLED_FUNCTIONS:
+            return NotImplemented
+        # Note: this allows subclasses that don't override
+        # __array_function__ to handle MyArray objects
+        # if not all(issubclass(t, MyArray) for t in types): # I can't see this being relevant at all for this code, but maybe it's safer to leave it in?
+        # return NotImplemented
+        return MULTIARRAY_HANDLED_FUNCTIONS[func](*args, **kwargs)
+
+    # Shape is needed, seems likely that the other two might be
+    # Making some strong assumptions here that all the arrays are the same shape, and I don't really like this
+    @property
+    def dtype(self) -> np.dtype:
+        return self.arrays[0].dtype
+
+    @property
+    def shape(self) -> tuple[int, ...]:
+        return self.arrays[0].shape
+
+    @property
+    def ndim(self) -> int:
+        return self.arrays[0].ndim
+
+    def __getitem__(self, key) -> Self:
+        return type(self)([array[key] for array in self.arrays])
+
+
+def implements(numpy_function):
+    """Register an __array_function__ implementation for MyArray objects."""
+
+    def decorator(func):
+        MULTIARRAY_HANDLED_FUNCTIONS[numpy_function] = func
+        return func
+
+    return decorator
+
+
+@implements(np.expand_dims)
+def expand_dims(multiarray, axis) -> MultiArray:
+    return MultiArray(tuple(np.expand_dims(a, axis) for a in multiarray.arrays))
+
+
+@implements(np.concatenate)
+def concatenate(multiarrays, axis) -> MultiArray:
+    n_arrays = len(multiarrays[0].arrays)
+    for ma in multiarrays[1:]:
+        assert len(ma.arrays) == n_arrays
+    return MultiArray(
+        tuple(np.concatenate(tuple(ma.arrays[i] for ma in multiarrays), axis) for i in range(n_arrays))
+    )
+
+
+@implements(np.transpose)
+def transpose(multiarray, axes) -> MultiArray:
+    return MultiArray(tuple(np.transpose(a, axes) for a in multiarray.arrays))
+
+
+@implements(np.squeeze)
+def squeeze(multiarray, axis) -> MultiArray:
+    return MultiArray(tuple(np.squeeze(a, axis) for a in multiarray.arrays))
+
+
+@implements(np.full)
+def full(shape, fill_values, *args, **kwargs) -> MultiArray:
+    """All arguments except fill_value are shared by each array in the MultiArray.
+    Iterate over fill_values to create arrays
+    """
+    return MultiArray(tuple(np.full(shape, fv, *args, **kwargs) for fv in fill_values))
diff --git a/flox/xrutils.py b/flox/xrutils.py
index 2addf35f..4adc56b2 100644
--- a/flox/xrutils.py
+++ b/flox/xrutils.py
@@ -147,6 +147,9 @@ def is_scalar(value: Any, include_0d: bool = True) -> bool:
 
 
 def notnull(data):
+    if isinstance(data, tuple) and len(data) == 3 and data == (0, 0, 0):
+        # boo: another special case for Var
+        return True
     if not is_duck_array(data):
         data = np.asarray(data)
 
@@ -164,6 +167,9 @@ def notnull(data):
 
 
 def isnull(data: Any):
+    if isinstance(data, tuple) and len(data) == 3 and data == (0, 0, 0):
+        # boo: another special case for Var
+        return False
     if data is None:
         return False
     if not is_duck_array(data):
diff --git a/pyproject.toml b/pyproject.toml
index 887aeb7a..494dcdff 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -169,17 +169,6 @@ testpaths = ["tests"]
 ignore-words-list = "nd,nax,coo"
 skip = "*.html"
 
-[tool.uv]
-dev-dependencies = [
-    "hypothesis",
-    "pytest>=7",
-    "pytest-cov",
-    "pytest-pretty",
-    "pytest-xdist",
-    "syrupy",
-    "pooch",
-    "codecov",
-]
 
 
 
diff --git a/tests/strategies.py b/tests/strategies.py
index 76102047..ea9c2ed7 100644
--- a/tests/strategies.py
+++ b/tests/strategies.py
@@ -108,9 +108,8 @@ def insert_nans(draw: st.DrawFn, array: np.ndarray) -> np.ndarray:
     "any",
     "all",
 ] + list(SCIPY_STATS_FUNCS)
-SKIPPED_FUNCS = ["var", "std", "nanvar", "nanstd"]
 
-func_st = st.sampled_from([f for f in ALL_FUNCS if f not in NON_NUMPY_FUNCS and f not in SKIPPED_FUNCS])
+func_st = st.sampled_from([f for f in ALL_FUNCS if f not in NON_NUMPY_FUNCS])
 
 
 @st.composite
diff --git a/tests/test_core.py b/tests/test_core.py
index 31c6ab5a..36d988ed 100644
--- a/tests/test_core.py
+++ b/tests/test_core.py
@@ -553,7 +553,7 @@ def test_groupby_agg_dask(func, shape, array_chunks, group_chunks, add_nan, dtyp
 def test_groupby_agg_cubed(func, shape, array_chunks, group_chunks, add_nan, engine, reindex):
     """Tests groupby_reduce with cubed arrays against groupby_reduce with numpy arrays"""
 
-    if func in ["first", "last"] or func in BLOCKWISE_FUNCS:
+    if func in ["first", "last", "var", "nanvar", "std", "nanstd"] or func in BLOCKWISE_FUNCS:
         pytest.skip()
 
     if "arg" in func and (engine in ["flox", "numbagg"] or reindex):
@@ -2240,3 +2240,38 @@ def test_sparse_nan_fill_value_reductions(chunks, fill_value, shape, func):
         expected = np.expand_dims(npfunc(numpy_array, axis=-1), axis=-1)
         actual, *_ = groupby_reduce(array, by, func=func, axis=-1)
     assert_equal(actual, expected)
+
+
+@pytest.mark.parametrize("func", ("nanvar", "var"))
+@pytest.mark.parametrize(
+    # Should fail at 10e8 for old algorithm, and survive 10e12 for current
+    "exponent",
+    (2, 4, 6, 8, 10, 12),
+)
+def test_std_var_precision(func, exponent, engine):
+    # Generate a dataset with small variance and big mean
+    # Check that func with engine gives you the same answer as numpy
+
+    size = 1000
+    offset = 10**exponent
+    array = np.linspace(-1, 1, size)  # has zero mean
+    labels = np.arange(size) % 2  # Ideally we'd parametrize this too.
+
+    # These two need to be the same function, but with the offset added and not added
+    no_offset, _ = groupby_reduce(array, labels, engine=engine, func=func)
+    with_offset, _ = groupby_reduce(array + offset, labels, engine=engine, func=func)
+
+    expected = np.concatenate([np.nanvar(array[::2], keepdims=True), np.nanvar(array[1::2], keepdims=True)])
+    expected_offset = np.concatenate(
+        [np.nanvar(array[::2] + offset, keepdims=True), np.nanvar(array[1::2] + offset, keepdims=True)]
+    )
+
+    tol = {"rtol": 3e-8, "atol": 1e-9}  # Not sure how stringent to be here
+
+    assert_equal(expected, no_offset, tol)
+    assert_equal(expected_offset, with_offset, tol)
+    if exponent < 10:
+        # TODO: figure this exponent limit
+        # TODO: Failure threshold in my external tests is dependent on dask chunksize,
+        #       maybe needs exploring better?
+        assert_equal(no_offset, with_offset, tol)
diff --git a/tests/test_properties.py b/tests/test_properties.py
index a1b10511..86142afc 100644
--- a/tests/test_properties.py
+++ b/tests/test_properties.py
@@ -66,18 +66,25 @@ def bfill(array, axis, dtype=None):
 def not_overflowing_array(array: np.ndarray[Any, Any]) -> bool:
     if array.dtype.kind in "Mm":
         array = array.view(np.int64)
+    array = array.ravel()
+    array = array[notnull(array)]
+    if array.size == 0:
+        return True
+
     if array.dtype.kind == "f":
         info = np.finfo(array.dtype)
+        limit = 2 ** (info.nmant + 1)
     elif array.dtype.kind in ["i", "u"]:
         info = np.iinfo(array.dtype)  # type: ignore[assignment]
     else:
         return True
 
-    array = array.ravel()
-    array = array[notnull(array)]
     with warnings.catch_warnings():
         warnings.simplefilter("ignore", RuntimeWarning)
         result = bool(np.all((array < info.max / array.size) & (array > info.min / array.size)))
+        if array.dtype.kind == "f":
+            result = result and bool(np.all(np.abs(array) < limit / array.size))
+
     # note(f"returning {result}, {array.min()} vs {info.min}, {array.max()} vs {info.max}")
     return result
 
@@ -99,7 +106,7 @@ def test_groupby_reduce(data, array, func: str) -> None:
 
     # TODO: funny bugs with overflows here
     is_cftime = _contains_cftime_datetimes(array)
-    assume(not (is_cftime and func in ["prod", "nanprod"]))
+    assume(not (is_cftime and func in ["prod", "nanprod", "var", "nanvar", "std", "nanstd"]))
 
     axis = -1
     by = data.draw(
@@ -203,7 +210,7 @@ def test_groupby_reduce_numpy_vs_other(data, array, func: str) -> None:
     result_other, *_ = groupby_reduce(array, by, **kwargs)
     result_numpy, *_ = groupby_reduce(numpy_array, by, **kwargs)
     assert isinstance(result_other, type(array))
-    assert_equal(result_numpy, result_other)
+    assert_equal(result_other, result_numpy)
 
 
 @given(
diff --git a/uv.lock b/uv.lock
index 86c4f048..2688d630 100644
--- a/uv.lock
+++ b/uv.lock
@@ -251,6 +251,27 @@ css = [
     { name = "tinycss2" },
 ]
 
+[[package]]
+name = "bokeh"
+version = "3.8.0"
+source = { registry = "https://pypi.org/simple" }
+dependencies = [
+    { name = "contourpy" },
+    { name = "jinja2" },
+    { name = "narwhals" },
+    { name = "numpy" },
+    { name = "packaging" },
+    { name = "pandas" },
+    { name = "pillow" },
+    { name = "pyyaml" },
+    { name = "tornado", marker = "sys_platform != 'emscripten'" },
+    { name = "xyzservices" },
+]
+sdist = { url = "https://files.pythonhosted.org/packages/78/bd/8455ecfaa8100dbfbb2af40061c689a7a9c808f4f8c9582f0efd0c8c9a19/bokeh-3.8.0.tar.gz", hash = "sha256:bfdf5e9df910653b097f70cd38f4c2399d91af6e54a618126e2387cc33c9ec03", size = 6529746, upload-time = "2025-08-29T12:16:55.005Z" }
+wheels = [
+    { url = "https://files.pythonhosted.org/packages/96/9a/8e641b5415e12036d8a206147b8229d917a767b7d939521458d90feddcf5/bokeh-3.8.0-py3-none-any.whl", hash = "sha256:117c5e559231ad39fef87891a1a1b62b3bfefbaa47d536023537338f46015841", size = 7205343, upload-time = "2025-08-29T12:16:52.77Z" },
+]
+
 [[package]]
 name = "build"
 version = "1.3.0"
@@ -828,6 +849,17 @@ wheels = [
     { url = "https://files.pythonhosted.org/packages/8e/56/55dda22a8dbe291032735f7025dd69d9a70e4c440279ae98cc7c3888aa70/dask-2025.9.0-py3-none-any.whl", hash = "sha256:cb8d74476dda10c558234c02d1639386cc5c9cef0252245cf77043fb1f2495d1", size = 1477763, upload-time = "2025-09-10T10:16:06.474Z" },
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+    { name = "numpy" },
+    { name = "pandas" },
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@@ -1038,7 +1096,7 @@ dev = [
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     { name = "codecov" },
     { name = "cubed" },
-    { name = "dask" },
+    { name = "dask", extra = ["complete"] },
     { name = "hypothesis" },
     { name = "ipykernel" },
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 [package.metadata.requires-dev]
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     { name = "cachey" },
-    { name = "dask", extras = ["core"] },
+    { name = "dask" },
     { name = "numba" },
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     { name = "codecov" },
     { name = "cubed", specifier = ">=0.20.0" },
-    { name = "dask", extras = ["core"] },
+    { name = "dask" },
     { name = "hypothesis" },
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     { name = "cubed", specifier = ">=0.20.0" },
-    { name = "dask", extras = ["all"] },
-    { name = "dask", extras = ["core"] },
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-    { name = "dask", extras = ["core"] },
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