diff --git a/src/QuadGK.jl b/src/QuadGK.jl
index 90c8681..8878092 100644
--- a/src/QuadGK.jl
+++ b/src/QuadGK.jl
@@ -40,14 +40,14 @@ struct InplaceIntegrand{F,R,RI}
     Ig::R
     Ik::R
     fx::R
-    Idiff::RI
+    Idiff::R
 
     # final result array
     I::RI
 end
 
 InplaceIntegrand(f!::F, I::RI, fx::R) where {F,RI,R} =
-    InplaceIntegrand{F,R,RI}(f!, similar(fx), similar(fx), similar(fx), similar(fx), fx, similar(I), I)
+    InplaceIntegrand{F,R,RI}(f!, similar(fx), similar(fx), similar(fx), similar(fx), fx, similar(fx), I)
 
 include("gausskronrod.jl")
 include("evalrule.jl")
diff --git a/src/adapt.jl b/src/adapt.jl
index 0a79d15..0459bb5 100644
--- a/src/adapt.jl
+++ b/src/adapt.jl
@@ -119,61 +119,77 @@ realone(x::Number) = one(x) isa Real
 # and pass transformed data to workfunc(f, s, tfunc)
 function handle_infinities(workfunc, f, s)
     s1, s2 = s[1], s[end]
+    u = float(real(oneunit(s1))) # the units of the segment
     if realone(s1) && realone(s2) # check for infinite or semi-infinite intervals
         inf1, inf2 = isinf(s1), isinf(s2)
         if inf1 || inf2
             if inf1 && inf2 # x = t/(1-t^2) coordinate transformation
-                return workfunc(t -> begin t2 = t*t; den = 1 / (1 - t2);
-                                            f(oneunit(s1)*t*den) * (1+t2)*den*den*oneunit(s1); end,
+                I, E = workfunc(t -> begin t2 = t*t; den = 1 / (1 - t2);
+                                            f(u*t*den) * (1+t2)*den*den; end,
                                 map(x -> isinf(x) ? (signbit(x) ? -one(x) : one(x)) : 2x / (oneunit(x)+hypot(oneunit(x),2x)), s),
-                                t -> oneunit(s1) * t / (1 - t^2))
+                                t -> u * t / (1 - t^2))
+                return u * I, u * E
             end
             let (s0,si) = inf1 ? (s2,s1) : (s1,s2) # let is needed for JuliaLang/julia#15276
                 if si < zero(si) # x = s0 - t/(1-t)
-                    return workfunc(t -> begin den = 1 / (1 - t);
-                                                f(s0 - oneunit(s1)*t*den) * den*den*oneunit(s1); end,
+                    I, E = workfunc(t -> begin den = 1 / (1 - t);
+                                                f(s0 - u*t*den) * den*den; end,
                                     reverse(map(x -> 1 / (1 + oneunit(x) / (s0 - x)), s)),
-                                    t -> s0 - oneunit(s1)*t/(1-t))
+                                    t -> s0 - u*t/(1-t))
+                    return u * I, u * E
                 else # x = s0 + t/(1-t)
-                    return workfunc(t -> begin den = 1 / (1 - t);
-                                                f(s0 + oneunit(s1)*t*den) * den*den*oneunit(s1); end,
+                    I, E = workfunc(t -> begin den = 1 / (1 - t);
+                                                f(s0 + u*t*den) * den*den; end,
                                     map(x -> 1 / (1 + oneunit(x) / (x - s0)), s),
-                                    t -> s0 + oneunit(s1)*t/(1-t))
+                                    t -> s0 + u*t/(1-t))
+                    return u * I, u * E
                 end
             end
         end
     end
-    return workfunc(f, s, identity)
+    I, E = workfunc(t -> f(t*u), map(x -> x/oneunit(x), s), identity)
+    return u * I, u * E
 end
 
 function handle_infinities(workfunc, f::InplaceIntegrand, s)
     s1, s2 = s[1], s[end]
+    result = f.I
+    u = float(real(oneunit(s1))) # the units of the segment
     if realone(s1) && realone(s2) # check for infinite or semi-infinite intervals
         inf1, inf2 = isinf(s1), isinf(s2)
         if inf1 || inf2
-            ftmp = f.fx # original integrand may have different units
             if inf1 && inf2 # x = t/(1-t^2) coordinate transformation
-                return workfunc(InplaceIntegrand((v, t) -> begin t2 = t*t; den = 1 / (1 - t2);
-                                            f.f!(ftmp, oneunit(s1)*t*den); v .= ftmp .* ((1+t2)*den*den*oneunit(s1)); end, f.I, f.fx * oneunit(s1)),
+                I, E = workfunc(InplaceIntegrand((v, t) -> begin t2 = t*t; den = 1 / (1 - t2);
+                                            f.f!(v, u*t*den); v .*= ((1+t2)*den*den); end, f.fg, f.fk, f.Ig, f.Ik, f.fx, f.Idiff, similar(f.fx)),
                                 map(x -> isinf(x) ? (signbit(x) ? -one(x) : one(x)) : 2x / (oneunit(x)+hypot(oneunit(x),2x)), s),
-                                t -> oneunit(s1) * t / (1 - t^2))
+                                t -> u * t / (1 - t^2))
+                result .= u .* I
+                return result, u * E
             end
             let (s0,si) = inf1 ? (s2,s1) : (s1,s2) # let is needed for JuliaLang/julia#15276
                 if si < zero(si) # x = s0 - t/(1-t)
-                    return workfunc(InplaceIntegrand((v, t) -> begin den = 1 / (1 - t);
-                                            f.f!(ftmp, s0 - oneunit(s1)*t*den); v .= ftmp .* (den * den * oneunit(s1)); end, f.I, f.fx * oneunit(s1)),
+                    I, E = workfunc(InplaceIntegrand((v, t) -> begin den = 1 / (1 - t);
+                                            f.f!(v, s0 - u*t*den); v .*= (den * den); end, f.fg, f.fk, f.Ig, f.Ik, f.fx, f.Idiff, similar(f.fx)),
                                     reverse(map(x -> 1 / (1 + oneunit(x) / (s0 - x)), s)),
-                                    t -> s0 - oneunit(s1)*t/(1-t))
+                                    t -> s0 - u*t/(1-t))
+                    result .= u .* I
+                    return result, u * E
                 else # x = s0 + t/(1-t)
-                    return workfunc(InplaceIntegrand((v, t) -> begin den = 1 / (1 - t);
-                                            f.f!(ftmp, s0 + oneunit(s1)*t*den); v .= ftmp .* (den * den * oneunit(s1)); end, f.I, f.fx * oneunit(s1)),
+                    I, E = workfunc(InplaceIntegrand((v, t) -> begin den = 1 / (1 - t);
+                                            f.f!(v, s0 + u*t*den); v .*= (den * den); end, f.fg, f.fk, f.Ig, f.Ik, f.fx, f.Idiff, similar(f.fx)),
                                     map(x -> 1 / (1 + oneunit(x) / (x - s0)), s),
-                                    t -> s0 + oneunit(s1)*t/(1-t))
+                                    t -> s0 + u*t/(1-t))
+                    result .= u .* I
+                    return result, u * E
                 end
             end
         end
     end
-    return workfunc(f, s, identity)
+    I, E = workfunc(InplaceIntegrand((y,t) -> f.f!(y, t*u), f.fg, f.fk, f.Ig, f.Ik, f.fx, f.Idiff, similar(f.fx)),
+                    map(x -> x/oneunit(x), s),
+                    identity)
+    result .= u .* I
+    return result, u * E
 end
 
 function check_endpoint_roundoff(a, b, x; throw_error::Bool=false)
@@ -254,8 +270,9 @@ quadgk(f, segs...; kws...) =
 
 function quadgk(f, segs::T...;
        atol=nothing, rtol=nothing, maxevals=10^7, order=7, norm=norm, segbuf=nothing) where {T}
+    utol = isnothing(atol) ? atol : atol/float(real(oneunit(T))) # remove units of domain
     handle_infinities(f, segs) do f, s, _
-        do_quadgk(f, s, order, atol, rtol, maxevals, norm, segbuf)
+        do_quadgk(f, s, order, utol, rtol, maxevals, norm, segbuf)
     end
 end
 
@@ -270,7 +287,9 @@ starting with the given `size`. The buffer can then be reused across multiple
 compatible calls to `quadgk(...)` to avoid repeated allocation.
 """
 function alloc_segbuf(domain_type=Float64, range_type=Float64, error_type=Float64; size=1)
-    Vector{Segment{domain_type, range_type, error_type}}(undef, size)
+    x = float(real(one(domain_type)))   # quadrature point type
+    err = oneunit(error_type)/oneunit(domain_type)  # error has units of the integral
+    Vector{Segment{typeof(x), range_type, typeof(err)}}(undef, size)
 end
 
 """
diff --git a/src/batch.jl b/src/batch.jl
index d4221b7..23b8e60 100644
--- a/src/batch.jl
+++ b/src/batch.jl
@@ -19,17 +19,19 @@ If `x` or `X` are not specified, `quadgk` internally creates a new `BatchIntegra
 user-supplied `y` buffer and a freshly-allocated `x` buffer based on the domain types. So,
 if you want to reuse the `x` buffer between calls, supply `{Y,X}` or pass `y,x` explicitly.
 """
-struct BatchIntegrand{Y,X,Ty<:AbstractVector{Y},Tx<:AbstractVector{X},F}
+struct BatchIntegrand{Y,X,Ty<:AbstractVector{Y},Tx<:AbstractVector{X},F,T}
     # in-place function f!(y, x) that takes an array of x values and outputs an array of results in-place
     f!::F
     y::Ty
     x::Tx
+    t::T
     max_batch::Int # maximum number of x to supply in parallel
 end
 
 function BatchIntegrand(f!, y::AbstractVector, x::AbstractVector=similar(y, Nothing); max_batch::Integer=typemax(Int))
     max_batch > 0 || throw(ArgumentError("max_batch must be positive"))
-    return BatchIntegrand(f!, y, x, max_batch)
+    X = eltype(x)
+    return BatchIntegrand(f!, y, x, X <: Nothing ? nothing : similar(x, typeof(one(X))), max_batch)
 end
 BatchIntegrand{Y,X}(f!; kws...) where {Y,X} = BatchIntegrand(f!, Y[], X[]; kws...)
 BatchIntegrand{Y}(f!; kws...) where {Y} = BatchIntegrand(f!, Y[]; kws...)
@@ -65,20 +67,20 @@ function evalrules(f::BatchIntegrand, s::NTuple{N}, x,w,gw, nrm) where {N}
     l = length(x)
     m = 2l-1    # evaluations per segment
     n = (N-1)*m # total evaluations
-    resize!(f.x, n)
+    resize!(f.t, n)
     resize!(f.y, n)
     for i in 1:(N-1)    # fill buffer with evaluation points
         a = s[i]; b = s[i+1]
         check_endpoint_roundoff(a, b, x, throw_error=true)
         c = convert(eltype(x), 0.5) * (b-a)
         o = (i-1)*m
-        f.x[l+o] = a + c
+        f.t[l+o] = a + c
         for j in 1:l-1
-            f.x[j+o] = a + (1 + x[j]) * c
-            f.x[m+1-j+o] = a + (1 - x[j]) * c
+            f.t[j+o] = a + (1 + x[j]) * c
+            f.t[m+1-j+o] = a + (1 - x[j]) * c
         end
     end
-    f.f!(f.y, f.x)  # evaluate integrand
+    f.f!(f.y, f.t)  # evaluate integrand
     return ntuple(Val(N-1)) do i
         return batchevalrule(view(f.y, (1+(i-1)*m):(i*m)), s[i], s[i+1], x,w,gw, nrm)
     end
@@ -105,7 +107,7 @@ function refine(f::BatchIntegrand, segs::Vector{T}, I, E, numevals, x,w,gw,n, at
         len > nsegs && DataStructures.percolate_down!(segs, 1, y, Reverse, len-nsegs)
     end
 
-    resize!(f.x, 2m*nsegs)
+    resize!(f.t, 2m*nsegs)
     resize!(f.y, 2m*nsegs)
     for i in 1:nsegs    # fill buffer with evaluation points
         s = segs[len-i+1]
@@ -114,15 +116,15 @@ function refine(f::BatchIntegrand, segs::Vector{T}, I, E, numevals, x,w,gw,n, at
             check_endpoint_roundoff(a, b, x) && return segs
             c = convert(eltype(x), 0.5) * (b-a)
             o = (2i-j)*m
-            f.x[l+o] = a + c
+            f.t[l+o] = a + c
             for k in 1:l-1
                 # early return if integrand evaluated at endpoints
-                f.x[k+o] = a + (1 + x[k]) * c
-                f.x[m+1-k+o] = a + (1 - x[k]) * c
+                f.t[k+o] = a + (1 + x[k]) * c
+                f.t[m+1-k+o] = a + (1 - x[k]) * c
             end
         end
     end
-    f.f!(f.y, f.x)
+    f.f!(f.y, f.t)
 
     resize!(segs, len+nsegs)
     for i in 1:nsegs    # evaluate segments and update estimates & heap
@@ -144,35 +146,39 @@ end
 
 function handle_infinities(workfunc, f::BatchIntegrand, s)
     s1, s2 = s[1], s[end]
+    u = float(real(oneunit(s1))) # the units of the segment
     if realone(s1) && realone(s2) # check for infinite or semi-infinite intervals
         inf1, inf2 = isinf(s1), isinf(s2)
         if inf1 || inf2
-            xtmp = f.x # buffer to store evaluation points
-            ytmp = f.y # original integrand may have different units
-            xbuf = similar(xtmp, typeof(one(eltype(f.x))))
-            ybuf = similar(ytmp, typeof(oneunit(eltype(f.y))*oneunit(s1)))
             if inf1 && inf2 # x = t/(1-t^2) coordinate transformation
-                return workfunc(BatchIntegrand((v, t) -> begin resize!(xtmp, length(t)); resize!(ytmp, length(v));
-                                            f.f!(ytmp, xtmp .= oneunit(s1) .* t ./ (1 .- t .* t)); v .= ytmp .* (1 .+ t .* t) .* oneunit(s1) ./ (1 .- t .* t) .^ 2; end, ybuf, xbuf, f.max_batch),
+                I, E = workfunc(BatchIntegrand((v, t) -> begin resize!(f.x, length(t));
+                                            f.f!(v, f.x .= u .* t ./ (1 .- t .* t)); v .*= (1 .+ t .* t) ./ (1 .- t .* t) .^ 2; end, f.y, f.x, f.t, f.max_batch),
                                 map(x -> isinf(x) ? (signbit(x) ? -one(x) : one(x)) : 2x / (oneunit(x)+hypot(oneunit(x),2x)), s),
-                                t -> oneunit(s1) * t / (1 - t^2))
+                                t -> u * t / (1 - t^2))
+                return u * I, u * E
             end
             let (s0,si) = inf1 ? (s2,s1) : (s1,s2) # let is needed for JuliaLang/julia#15276
                 if si < zero(si) # x = s0 - t/(1-t)
-                    return workfunc(BatchIntegrand((v, t) -> begin resize!(xtmp, length(t)); resize!(ytmp, length(v));
-                                            f.f!(ytmp, xtmp .= s0 .- oneunit(s1) .* t ./ (1 .- t)); v .= ytmp .* oneunit(s1) ./ (1 .- t) .^ 2; end, ybuf, xbuf, f.max_batch),
+                    I, E = workfunc(BatchIntegrand((v, t) -> begin resize!(f.x, length(t));
+                                            f.f!(v, f.x .= s0 .- u .* t ./ (1 .- t)); v ./= (1 .- t) .^ 2; end, f.y, f.x, f.t, f.max_batch),
                                     reverse(map(x -> 1 / (1 + oneunit(x) / (s0 - x)), s)),
-                                    t -> s0 - oneunit(s1)*t/(1-t))
+                                    t -> s0 - u*t/(1-t))
+                    return u * I, u * E
                 else # x = s0 + t/(1-t)
-                    return workfunc(BatchIntegrand((v, t) -> begin resize!(xtmp, length(t)); resize!(ytmp, length(v));
-                                            f.f!(ytmp, xtmp .= s0 .+ oneunit(s1) .* t ./ (1 .- t)); v .= ytmp .* oneunit(s1) ./ (1 .- t) .^ 2; end, ybuf, xbuf, f.max_batch),
+                    I, E = workfunc(BatchIntegrand((v, t) -> begin resize!(f.x, length(t));
+                                            f.f!(v, f.x .= s0 .+ u .* t ./ (1 .- t)); v ./= (1 .- t) .^ 2; end, f.y, f.x, f.t, f.max_batch),
                                     map(x -> 1 / (1 + oneunit(x) / (x - s0)), s),
-                                    t -> s0 + oneunit(s1)*t/(1-t))
+                                    t -> s0 + u*t/(1-t))
+                    return u * I, u * E
                 end
             end
         end
     end
-    return workfunc(f, s, identity)
+    I, E = workfunc(BatchIntegrand((y, t) -> begin resize!(f.x, length(t));
+                    f.f!(y, f.x .= u .* t); end, f.y, f.x, f.t, f.max_batch),
+                    map(x -> x/oneunit(x), s),
+                    identity)
+    return u * I, u * E
 end
 
 """
@@ -194,6 +200,6 @@ simultaneously. In particular, there are two differences from `quadgk`
 """
 function quadgk(f::BatchIntegrand{Y,Nothing}, segs::T...; kws...) where {Y,T}
     FT = float(T) # the gk points are floating-point
-    g = BatchIntegrand(f.f!, f.y, similar(f.x, FT), f.max_batch)
+    g = BatchIntegrand(f.f!, f.y, similar(f.x, FT), similar(f.x, typeof(float(one(FT)))), f.max_batch)
     return quadgk(g, segs...; kws...)
 end
diff --git a/test/runtests.jl b/test/runtests.jl
index 8c56014..43f915d 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -41,15 +41,23 @@ module Test19626
     end
 
     # Following definitions needed for quadgk to work with MockQuantity
-    import Base: +, -, *, abs, isnan, isinf, isless, float
+    import Base: +, -, *, /, abs, isnan, isinf, isless, float, one, real, signbit
     +(a::MockQuantity, b::MockQuantity) = MockQuantity(a.val+b.val)
     -(a::MockQuantity, b::MockQuantity) = MockQuantity(a.val-b.val)
+    -(a::MockQuantity) = MockQuantity(-a.val)
     *(a::MockQuantity, b::Number) = MockQuantity(a.val*b)
+    *(a::Number, b::MockQuantity) = MockQuantity(a*b.val)
+    /(a::MockQuantity, b::Number) = MockQuantity(a.val/b)
+    /(a::MockQuantity, b::MockQuantity) = a.val/b.val
     abs(a::MockQuantity) = MockQuantity(abs(a.val))
     float(a::MockQuantity) = a
     isnan(a::MockQuantity) = isnan(a.val)
     isinf(a::MockQuantity) = isinf(a.val)
     isless(a::MockQuantity, b::MockQuantity) = isless(a.val, b.val)
+    one(::Type{MockQuantity}) = one(fieldtype(MockQuantity, :val))
+    one(a::MockQuantity) = one(a.val)
+    real(a::MockQuantity) = MockQuantity(real(a.val))
+    signbit(a::MockQuantity) = signbit(a.val)
 
     # isapprox only needed for test purposes
     Base.isapprox(a::MockQuantity, b::MockQuantity) = isapprox(a.val, b.val)
@@ -57,6 +65,27 @@ module Test19626
     # Test physical quantity-valued functions
     @test QuadGK.quadgk(x->MockQuantity(x), 0.0, 1.0, atol=MockQuantity(0.0))[1] ≈
         MockQuantity(0.5)
+
+    # Test that quantities work with infinity transformations and segbufs
+    # for all quadgk interfaces
+    lims = [(-1.0, 1.0), (-Inf, 0.0), (0.0, Inf), (-Inf, Inf)]
+    ulims = map(x -> map(MockQuantity, x), lims)
+    for (lb, ub) in ulims
+        ## function
+        f = x -> 1/(1+(x/MockQuantity(1.0))^2)
+        buf = QuadGK.alloc_segbuf(MockQuantity, Float64, MockQuantity)
+        @test QuadGK.quadgk(f, lb, ub, atol=MockQuantity(0.0))[1] ≈
+                QuadGK.quadgk(f, lb, ub, atol=MockQuantity(0.0), segbuf=buf)[1]
+        ## inplace
+        fiip = (y, x) -> y[1] = 1/(1+(x/MockQuantity(1.0))^2)
+        ibuf = QuadGK.alloc_segbuf(MockQuantity, Array{Float64,1}, MockQuantity)
+        @test QuadGK.quadgk!(fiip, [MockQuantity(0.0)], lb, ub, atol=MockQuantity(0.0), norm=abs∘first)[1][] ≈
+                QuadGK.quadgk!(fiip, [MockQuantity(0.0)], lb, ub, atol=MockQuantity(0.0), norm=abs∘getindex, segbuf=ibuf)[1][]
+        ## batch
+        fbatch = BatchIntegrand{Float64}((y, x) -> y .= 1 ./ (1 .+ (x ./ MockQuantity(1.0)) .^ 2))
+        @test QuadGK.quadgk(fbatch, lb, ub, atol=MockQuantity(0.0))[1] ≈
+                QuadGK.quadgk(fbatch, lb, ub, atol=MockQuantity(0.0), segbuf=buf)[1]
+    end
 end
 
 @testset "inference" begin
@@ -312,7 +341,7 @@ end
     end
 
     # test constructors
-    ref = BatchIntegrand(f!, Float64[], Nothing[], typemax(Int))
+    ref = BatchIntegrand(f!, Float64[], Nothing[], nothing, typemax(Int))
     for b in (
         BatchIntegrand(f!, Float64[]),
         BatchIntegrand(f!, Float64[], Nothing[]),