diff --git a/base/dates/rounding.jl b/base/dates/rounding.jl
index 6a4a40d38ae13..d8efe47f1a94c 100644
--- a/base/dates/rounding.jl
+++ b/base/dates/rounding.jl
@@ -7,6 +7,9 @@ const DATETIMEEPOCH = value(DateTime(0))
 # According to ISO 8601, the first day of the first week of year 0000 is 0000-01-03
 const WEEKEPOCH = value(Date(0, 1, 3))
 
+const ConvertiblePeriod = Union{TimePeriod, Week, Day}
+const TimeTypeOrPeriod = Union{TimeType, ConvertiblePeriod}
+
 """
     epochdays2date(days) -> Date
 
@@ -76,6 +79,35 @@ function Base.floor(dt::DateTime, p::TimePeriod)
     return epochms2datetime(milliseconds - mod(milliseconds, value(Millisecond(p))))
 end
 
+"""
+    floor(x::Period, precision::T) where T <: Union{TimePeriod, Week, Day} -> T
+
+Rounds `x` down to the nearest multiple of `precision`. If `x` and `precision` are different
+subtypes of `Period`, the return value will have the same type as `precision`.
+
+For convenience, `precision` may be a type instead of a value: `floor(x, Dates.Hour)` is a
+shortcut for `floor(x, Dates.Hour(1))`.
+
+```jldoctest
+julia> floor(Dates.Day(16), Dates.Week)
+2 weeks
+
+julia> floor(Dates.Minute(44), Dates.Minute(15))
+30 minutes
+
+julia> floor(Dates.Hour(36), Dates.Day)
+1 day
+```
+
+Rounding to a `precision` of `Month`s or `Year`s is not supported, as these `Period`s are of
+inconsistent length.
+"""
+function Base.floor(x::ConvertiblePeriod, precision::T) where T <: ConvertiblePeriod
+    value(precision) < 1 && throw(DomainError(precision))
+    _x, _precision = promote(x, precision)
+    return T(_x - mod(_x, _precision))
+end
+
 """
     floor(dt::TimeType, p::Period) -> TimeType
 
@@ -121,6 +153,34 @@ function Base.ceil(dt::TimeType, p::Period)
     return (dt == f) ? f : f + p
 end
 
+"""
+    ceil(x::Period, precision::T) where T <: Union{TimePeriod, Week, Day} -> T
+
+Rounds `x` up to the nearest multiple of `precision`. If `x` and `precision` are different
+subtypes of `Period`, the return value will have the same type as `precision`.
+
+For convenience, `precision` may be a type instead of a value: `ceil(x, Dates.Hour)` is a
+shortcut for `ceil(x, Dates.Hour(1))`.
+
+```jldoctest
+julia> ceil(Dates.Day(16), Dates.Week)
+3 weeks
+
+julia> ceil(Dates.Minute(44), Dates.Minute(15))
+45 minutes
+
+julia> ceil(Dates.Hour(36), Dates.Day)
+3 days
+```
+
+Rounding to a `precision` of `Month`s or `Year`s is not supported, as these `Period`s are of
+inconsistent length.
+"""
+function Base.ceil(x::ConvertiblePeriod, precision::ConvertiblePeriod)
+    f = floor(x, precision)
+    return (x == f) ? f : f + precision
+end
+
 """
     floorceil(dt::TimeType, p::Period) -> (TimeType, TimeType)
 
@@ -132,6 +192,17 @@ function floorceil(dt::TimeType, p::Period)
     return f, (dt == f) ? f : f + p
 end
 
+"""
+    floorceil(x::Period, precision::T) where T <: Union{TimePeriod, Week, Day} -> (T, T)
+
+Simultaneously return the `floor` and `ceil` of `Period` at resolution `p`.  More efficient
+than calling both `floor` and `ceil` individually.
+"""
+function floorceil(x::ConvertiblePeriod, precision::ConvertiblePeriod)
+    f = floor(x, precision)
+    return f, (x == f) ? f : f + precision
+end
+
 """
     round(dt::TimeType, p::Period, [r::RoundingMode]) -> TimeType
 
@@ -160,21 +231,55 @@ function Base.round(dt::TimeType, p::Period, r::RoundingMode{:NearestTiesUp})
     return (dt - f) < (c - dt) ? f : c
 end
 
-Base.round(dt::TimeType, p::Period, r::RoundingMode{:Down}) = Base.floor(dt, p)
-Base.round(dt::TimeType, p::Period, r::RoundingMode{:Up}) = Base.ceil(dt, p)
+"""
+    round(x::Period, precision::T, [r::RoundingMode]) where T <: Union{TimePeriod, Week, Day} -> T
+
+Rounds `x` to the nearest multiple of `precision`. If `x` and `precision` are different
+subtypes of `Period`, the return value will have the same type as `precision`. By default
+(`RoundNearestTiesUp`), ties (e.g., rounding 90 minutes to the nearest hour) will be rounded
+up.
+
+For convenience, `precision` may be a type instead of a value: `round(x, Dates.Hour)` is a
+shortcut for `round(x, Dates.Hour(1))`.
+
+```jldoctest
+julia> round(Dates.Day(16), Dates.Week)
+2 weeks
+
+julia> round(Dates.Minute(44), Dates.Minute(15))
+45 minutes
+
+julia> round(Dates.Hour(36), Dates.Day)
+3 days
+```
+
+Valid rounding modes for `round(::Period, ::T, ::RoundingMode)` are `RoundNearestTiesUp`
+(default), `RoundDown` (`floor`), and `RoundUp` (`ceil`).
+
+Rounding to a `precision` of `Month`s or `Year`s is not supported, as these `Period`s are of
+inconsistent length.
+"""
+function Base.round(x::ConvertiblePeriod, precision::ConvertiblePeriod, r::RoundingMode{:NearestTiesUp})
+    f, c = floorceil(x, precision)
+    _x, _f, _c = promote(x, f, c)
+    return (_x - _f) < (_c - _x) ? f : c
+end
+
+Base.round(x::TimeTypeOrPeriod, p::Period, r::RoundingMode{:Down}) = Base.floor(x, p)
+Base.round(x::TimeTypeOrPeriod, p::Period, r::RoundingMode{:Up}) = Base.ceil(x, p)
 
 # No implementation of other `RoundingMode`s: rounding to nearest "even" is skipped because
 # "even" is not defined for Period; rounding toward/away from zero is skipped because ISO
 # 8601's year 0000 is not really "zero".
-Base.round(::TimeType, p::Period, ::RoundingMode) = throw(DomainError(p))
+Base.round(::TimeTypeOrPeriod, p::Period, ::RoundingMode) = throw(DomainError(p))
 
 # Default to RoundNearestTiesUp.
-Base.round(dt::TimeType, p::Period) = Base.round(dt, p, RoundNearestTiesUp)
+Base.round(x::TimeTypeOrPeriod, p::Period) = Base.round(x, p, RoundNearestTiesUp)
 
 # Make rounding functions callable using Period types in addition to values.
-Base.floor(dt::TimeType, p::Type{<:Period}) = Base.floor(dt, p(1))
-Base.ceil(dt::TimeType, p::Type{<:Period}) = Base.ceil(dt, p(1))
+Base.floor(x::TimeTypeOrPeriod, ::Type{P}) where P <: Period = Base.floor(x, oneunit(P))
+Base.ceil(x::TimeTypeOrPeriod, ::Type{P}) where P <: Period = Base.ceil(x, oneunit(P))
 
-function Base.round(dt::TimeType, p::Type{<:Period}, r::RoundingMode=RoundNearestTiesUp)
-    return Base.round(dt, p(1), r)
+function Base.round(x::TimeTypeOrPeriod, ::Type{P}, r::RoundingMode=RoundNearestTiesUp) where P <: Period
+    return Base.round(x, oneunit(P), r)
 end
diff --git a/doc/src/stdlib/dates.md b/doc/src/stdlib/dates.md
index a7ebd9f3d64dd..b7ff1f950bda0 100644
--- a/doc/src/stdlib/dates.md
+++ b/doc/src/stdlib/dates.md
@@ -132,6 +132,14 @@ Base.ceil(::Base.Dates.TimeType, ::Base.Dates.Period)
 Base.round(::Base.Dates.TimeType, ::Base.Dates.Period, ::RoundingMode{:NearestTiesUp})
 ```
 
+Most `Period` values can also be rounded to a specified resolution:
+
+```@docs
+Base.floor(::Base.Dates.ConvertiblePeriod, ::T) where T <: Base.Dates.ConvertiblePeriod
+Base.ceil(::Base.Dates.ConvertiblePeriod, ::Base.Dates.ConvertiblePeriod)
+Base.round(::Base.Dates.ConvertiblePeriod, ::Base.Dates.ConvertiblePeriod, ::RoundingMode{:NearestTiesUp})
+```
+
 The following functions are not exported:
 
 ```@docs
diff --git a/test/dates/rounding.jl b/test/dates/rounding.jl
index b68c14ba80eb4..b12d1a757a992 100644
--- a/test/dates/rounding.jl
+++ b/test/dates/rounding.jl
@@ -133,7 +133,7 @@ end
     @test_throws DomainError round(dt, Dates.Day, RoundToZero)
     @test round(dt, Dates.Day) == round(dt, Dates.Day, RoundNearestTiesUp)
 end
-@testset "Rounding to invalid resolutions" begin
+@testset "Rounding datetimes to invalid resolutions" begin
     dt = Dates.DateTime(2016, 2, 28, 12, 15)
     for p in [Dates.Year, Dates.Month, Dates.Week, Dates.Day, Dates.Hour]
         local p
@@ -144,3 +144,77 @@ end
         end
     end
 end
+@testset "Rounding for periods" begin
+    x = Dates.Second(172799)
+    @test floor(x, Dates.Week) == Dates.Week(0)
+    @test floor(x, Dates.Day) == Dates.Day(1)
+    @test floor(x, Dates.Hour) == Dates.Hour(47)
+    @test floor(x, Dates.Minute) == Dates.Minute(2879)
+    @test floor(x, Dates.Second) == Dates.Second(172799)
+    @test floor(x, Dates.Millisecond) == Dates.Millisecond(172799000)
+    @test ceil(x, Dates.Week) == Dates.Week(1)
+    @test ceil(x, Dates.Day) == Dates.Day(2)
+    @test ceil(x, Dates.Hour) == Dates.Hour(48)
+    @test ceil(x, Dates.Minute) == Dates.Minute(2880)
+    @test ceil(x, Dates.Second) == Dates.Second(172799)
+    @test ceil(x, Dates.Millisecond) == Dates.Millisecond(172799000)
+    @test round(x, Dates.Week) == Dates.Week(0)
+    @test round(x, Dates.Day) == Dates.Day(2)
+    @test round(x, Dates.Hour) == Dates.Hour(48)
+    @test round(x, Dates.Minute) == Dates.Minute(2880)
+    @test round(x, Dates.Second) == Dates.Second(172799)
+    @test round(x, Dates.Millisecond) == Dates.Millisecond(172799000)
+
+    x = Dates.Nanosecond(2000999999)
+    @test floor(x, Dates.Second) == Dates.Second(2)
+    @test floor(x, Dates.Millisecond) == Dates.Millisecond(2000)
+    @test floor(x, Dates.Microsecond) == Dates.Microsecond(2000999)
+    @test floor(x, Dates.Nanosecond) == x
+    @test ceil(x, Dates.Second) == Dates.Second(3)
+    @test ceil(x, Dates.Millisecond) == Dates.Millisecond(2001)
+    @test ceil(x, Dates.Microsecond) == Dates.Microsecond(2001000)
+    @test ceil(x, Dates.Nanosecond) == x
+    @test round(x, Dates.Second) == Dates.Second(2)
+    @test round(x, Dates.Millisecond) == Dates.Millisecond(2001)
+    @test round(x, Dates.Microsecond) == Dates.Microsecond(2001000)
+    @test round(x, Dates.Nanosecond) == x
+end
+@testset "Rounding for periods that should not need rounding" begin
+    for x in [Dates.Week(3), Dates.Day(14), Dates.Second(604800)]
+        local x
+        for p in [Dates.Week, Dates.Day, Dates.Hour, Dates.Second, Dates.Millisecond, Dates.Microsecond, Dates.Nanosecond]
+            local p
+            @test floor(x, p) == p(x)
+            @test ceil(x, p) == p(x)
+        end
+    end
+end
+@testset "Various available RoundingModes for periods" begin
+    x = Dates.Hour(36)
+    @test round(x, Dates.Day, RoundNearestTiesUp) == Dates.Day(2)
+    @test round(x, Dates.Day, RoundUp) == Dates.Day(2)
+    @test round(x, Dates.Day, RoundDown) == Dates.Day(1)
+    @test_throws DomainError round(x, Dates.Day, RoundNearest)
+    @test_throws DomainError round(x, Dates.Day, RoundNearestTiesAway)
+    @test_throws DomainError round(x, Dates.Day, RoundToZero)
+    @test round(x, Dates.Day) == round(x, Dates.Day, RoundNearestTiesUp)
+end
+@testset "Rounding periods to invalid resolutions" begin
+    x = Dates.Hour(86399)
+    for p in [Dates.Week, Dates.Day, Dates.Hour, Dates.Second, Dates.Millisecond, Dates.Microsecond, Dates.Nanosecond]
+        local p
+        for v in [-1, 0]
+            @test_throws DomainError floor(x, p(v))
+            @test_throws DomainError ceil(x, p(v))
+            @test_throws DomainError round(x, p(v))
+        end
+    end
+    for p in [Dates.Year, Dates.Month]
+        local p
+        for v in [-1, 0, 1]
+            @test_throws MethodError floor(x, p(v))
+            @test_throws MethodError ceil(x, p(v))
+            @test_throws DomainError round(x, p(v))
+        end
+    end
+end