diff --git a/resources/css/components/timepicker.css b/resources/css/components/timepicker.css
index 414a4b48..da35f8d4 100644
--- a/resources/css/components/timepicker.css
+++ b/resources/css/components/timepicker.css
@@ -11,7 +11,9 @@
  *       [data-timepicker-display] the time selector: hour and minute boxes 96×80 (display-large,
  *                                 small corner; primary-container when selected, otherwise
  *                                 surface-container-highest), a 24px separator, and the period
- *                                 selector 52×80 beside them, 4px away
+ *                                 selector 52×80 beside them, 4px away. On a 24-hour clock
+ *                                 (data-cycle="24") there is no period selector and the boxes are
+ *                                 114px, TimeSelector24HVerticalContainerWidth.
  *       [data-timepicker-dial]    256px, surface-container-highest; numbers in body-large at radius
  *                                 101 (the 24-hour inner ring at 69), a primary selector — a 2px line,
  *                                 an 8px centre and a 48px handle — with the number under the handle
@@ -20,9 +22,11 @@
  *                                 "Minute" (or the error) below in body-small, the period 52×72
  *     [data-timepicker-actions]   a 48px row: the mode toggle, then Cancel and OK
  *
- * The period selector is Compose's current one (ComposeMaterial3Flags.isUpdatedTimepickerToggleEnabled,
- * on by default): two toggle buttons 4px apart, round and surface-container-lowest when off, a 12px
- * corner and primary-container with a bold label when on, not the outlined pair of the tokens.
+ * The period selector keeps Compose's current shape (ComposeMaterial3Flags.isUpdatedTimepickerToggleEnabled,
+ * on by default): two buttons 4px apart, round and surface-container-lowest when off, a 12px corner
+ * when on, not the outlined pair of the tokens. The selected colour is M3's own tertiary-container
+ * with a bold label (PeriodSelectorSelectedContainerColor), which keeps AM/PM apart from the
+ * primary-container hour and minute boxes. They are radios, so the state is `aria-checked`.
  *
  * In a landscape window with no room for the upright dial the dial variant lies on its side, as
  * Compose's HorizontalTimePicker does: the display with the period selector (216×38, 16px under it)
@@ -130,6 +134,13 @@
         color: var(--md-sys-color-on-primary-container);
     }
 
+    /* A 24-hour clock has no period selector beside the boxes, and M3 widens them into the room
+       (TimePickerTokens.TimeSelector24HVerticalContainerWidth = 114dp). Landscape keeps 96px: the
+       display is a 216px column there. */
+    [data-timepicker-display][data-cycle="24"] [data-timepicker-box] {
+        width: 7.125rem;
+    }
+
     [data-timepicker-separator] {
         display: grid;
         place-items: center;
@@ -165,20 +176,22 @@
     }
 
     [data-timepicker-period] > button:active,
-    [data-timepicker-period] > button[aria-pressed="true"] {
+    [data-timepicker-period] > button[aria-checked="true"] {
         border-radius: 0.75rem;
     }
 
-    [data-timepicker-period] > button[aria-pressed="true"] {
-        background-color: var(--md-sys-color-primary-container);
-        color: var(--md-sys-color-on-primary-container);
+    /* Tertiary, not the primary the hour and minute boxes take: M3 gives the two selectors different
+       emphases (PeriodSelectorSelectedContainerColor = TertiaryContainer). */
+    [data-timepicker-period] > button[aria-checked="true"] {
+        background-color: var(--md-sys-color-tertiary-container);
+        color: var(--md-sys-color-on-tertiary-container);
         font-weight: var(--md-ref-typeface-weight-bold);
     }
 
     [data-timepicker-period] > button:disabled {
         cursor: default;
         color: color-mix(in srgb, var(--md-sys-color-on-surface) 38%, transparent);
-        background-color: color-mix(in srgb, var(--md-sys-color-on-surface) 10%, transparent);
+        background-color: color-mix(in srgb, var(--md-sys-color-on-surface) 12%, transparent);
     }
 
     /* ---- The dial ----------------------------------------------------------------------------- */
@@ -436,6 +449,10 @@
             margin: 0;
         }
 
+        [data-timepicker-surface][data-mode="dial"] [data-timepicker-display][data-cycle="24"] [data-timepicker-box] {
+            width: 6rem;
+        }
+
         [data-timepicker-surface][data-mode="dial"] [data-timepicker-display] [data-timepicker-period] {
             flex-direction: row;
             width: 13.5rem;
diff --git a/resources/js/timepicker.js b/resources/js/timepicker.js
index 9c4b69bb..85ff7558 100644
--- a/resources/js/timepicker.js
+++ b/resources/js/timepicker.js
@@ -380,6 +380,21 @@ document.addEventListener('alpine:init', () => {
             this.aim()
         },
 
+        /**
+         * AM and PM are a radio group, which M3's labelling table asks for: an arrow key moves to
+         * the other option and selects it, and focus follows, as WAI-ARIA's radio group does.
+         */
+        movePeriod(event) {
+            const pm = !this.isPm
+
+            if (!this.periodAllowed(pm)) {
+                return
+            }
+
+            this.setPeriod(pm)
+            event.currentTarget.querySelector(`[data-timepicker-period-option="${pm ? 'pm' : 'am'}"]`)?.focus()
+        },
+
         /** The allowed time in a period nearest to `time` (periodAllowed has said there is one). */
         nearestInPeriod(pm, time) {
             let best = null
diff --git a/resources/views/components/timepicker.blade.php b/resources/views/components/timepicker.blade.php
index 14fa9b11..81de4e7a 100644
--- a/resources/views/components/timepicker.blade.php
+++ b/resources/views/components/timepicker.blade.php
@@ -31,14 +31,16 @@
      TimePickerTokens and TimeInputTokens — a surface-container-high dialog with an extra-large
      corner and elevation 3, a 256dp surface-container-highest dial with body-large numbers, a primary
      selector with a 48dp handle, a 2dp line and an 8dp centre, 96×80 time selector boxes in
-     display-large (primary-container when selected), 96×72 time fields in display-medium — and
-     TimePicker.kt and TimePickerDialog.kt for the layout, the 24-hour inner ring (12–23, at 69dp;
-     00–11 outside at 101dp, as Material Components for Android labels them too), the gestures, the
-     move on to minutes and the error texts. The period selector is Compose's current default
-     (`isUpdatedTimepickerToggleEnabled`): two separate shape-morphing toggle buttons in
-     primary-container, not the outlined pair its tokens still describe. The dial's numbers are
-     aria-hidden; the dial is a `slider` whose value text names the hour or minute. The dialog is
-     `wire:ignore`, so a Livewire render never closes an open picker or resets its draft. --}}
+     display-large (primary-container when selected; 114dp wide on a 24-hour clock, where there is no
+     period selector beside them, per TimeSelector24HVerticalContainerWidth), 96×72 time fields in
+     display-medium — and TimePicker.kt and TimePickerDialog.kt for the layout, the 24-hour inner
+     ring (12–23, at 69dp; 00–11 outside at 101dp, as Material Components for Android labels them
+     too), the gestures, the move on to minutes and the error texts. The period selector keeps
+     Compose's current default shape morph (`isUpdatedTimepickerToggleEnabled`) but M3's own
+     tertiary-container, which is what holds hour/minute (primary-container) and AM/PM apart; it is a
+     radio group, as M3's labelling table says, so the arrows move between AM and PM. The dial's
+     numbers are aria-hidden; the dial is a `slider` whose value text names the hour or minute. The
+     dialog is `wire:ignore`, so a Livewire render never closes an open picker or resets its draft. --}}
 
 @props([
     'label' => null,
@@ -211,7 +213,7 @@
             <h2 id="{{ $id }}-title" data-timepicker-title x-text="mode === 'dial' ? @js(__('Select time')) : @js(__('Enter time'))">{{ __('Select time') }}</h2>
 
             <div data-timepicker-picker>
-                <div data-timepicker-display>
+                <div data-timepicker-display x-bind:data-cycle="is24 ? '24' : '12'">
                     <div data-timepicker-numbers>
                         <button
                             type="button"
@@ -236,13 +238,25 @@
                         ></button>
                     </div>
 
-                    <div data-timepicker-period role="group" aria-label="{{ __('Select AM or PM') }}" x-show="! is24">
+                    <div
+                        data-timepicker-period
+                        role="radiogroup"
+                        aria-label="{{ __('Select AM or PM') }}"
+                        x-show="! is24"
+                        x-on:keydown.arrow-right.prevent="movePeriod($event)"
+                        x-on:keydown.arrow-left.prevent="movePeriod($event)"
+                        x-on:keydown.arrow-down.prevent="movePeriod($event)"
+                        x-on:keydown.arrow-up.prevent="movePeriod($event)"
+                    >
                         @foreach ([false => 'am', true => 'pm'] as $pm => $period)
                             <button
                                 type="button"
                                 data-timepicker-period-option="{{ $period }}"
                                 class="state-layer focus-ring"
-                                x-bind:aria-pressed="({{ $pm ? '' : '! ' }}isPm).toString()"
+                                role="radio"
+                                aria-checked="false"
+                                x-bind:aria-checked="({{ $pm ? '' : '! ' }}isPm).toString()"
+                                x-bind:tabindex="({{ $pm ? '' : '! ' }}isPm) ? 0 : -1"
                                 x-bind:disabled="! periodAllowed({{ $pm ? 'true' : 'false' }})"
                                 x-on:click="setPeriod({{ $pm ? 'true' : 'false' }})"
                                 x-text="periods[{{ (int) $pm }}]"
@@ -330,13 +344,25 @@
                         </div>
                     @endforeach
 
-                    <div data-timepicker-period role="group" aria-label="{{ __('Select AM or PM') }}" x-show="! is24">
+                    <div
+                        data-timepicker-period
+                        role="radiogroup"
+                        aria-label="{{ __('Select AM or PM') }}"
+                        x-show="! is24"
+                        x-on:keydown.arrow-right.prevent="movePeriod($event)"
+                        x-on:keydown.arrow-left.prevent="movePeriod($event)"
+                        x-on:keydown.arrow-down.prevent="movePeriod($event)"
+                        x-on:keydown.arrow-up.prevent="movePeriod($event)"
+                    >
                         @foreach ([false => 'am', true => 'pm'] as $pm => $period)
                             <button
                                 type="button"
                                 data-timepicker-period-option="{{ $period }}"
                                 class="state-layer focus-ring"
-                                x-bind:aria-pressed="({{ $pm ? '' : '! ' }}isPm).toString()"
+                                role="radio"
+                                aria-checked="false"
+                                x-bind:aria-checked="({{ $pm ? '' : '! ' }}isPm).toString()"
+                                x-bind:tabindex="({{ $pm ? '' : '! ' }}isPm) ? 0 : -1"
                                 x-bind:disabled="! periodAllowed({{ $pm ? 'true' : 'false' }})"
                                 x-on:click="setPeriod({{ $pm ? 'true' : 'false' }})"
                                 x-text="periods[{{ (int) $pm }}]"
diff --git a/tests/Browser/TimepickerTest.php b/tests/Browser/TimepickerTest.php
index 97c8c2cd..72461185 100644
--- a/tests/Browser/TimepickerTest.php
+++ b/tests/Browser/TimepickerTest.php
@@ -82,7 +82,7 @@ it('opens the dial on the hour, as the bound time says', function () {
         ->assertAttribute('#meeting-dialog [data-timepicker-box="hour"]', 'aria-pressed', 'true')
         ->assertSeeIn('#meeting-dialog [data-timepicker-box="hour"]', '09')
         ->assertSeeIn('#meeting-dialog [data-timepicker-box="minute"]', '30')
-        ->assertAttribute('#meeting-dialog [data-timepicker-display] [data-timepicker-period-option="am"]', 'aria-pressed', 'true')
+        ->assertAttribute('#meeting-dialog [data-timepicker-display] [data-timepicker-period-option="am"]', 'aria-checked', 'true')
         ->assertAttribute('#meeting-dialog [data-timepicker-dial]', 'aria-valuenow', '9')
         ->assertScript('document.activeElement === '.inPicker('meeting', '[data-timepicker-dial]'));
 });
@@ -131,7 +131,7 @@ it('turns three o\'clock into 15 with PM', function () {
     timeProbe()
         ->click('#meeting')
         ->click('#meeting-dialog [data-timepicker-display] [data-timepicker-period-option="pm"]')
-        ->assertAttribute('#meeting-dialog [data-timepicker-display] [data-timepicker-period-option="pm"]', 'aria-pressed', 'true')
+        ->assertAttribute('#meeting-dialog [data-timepicker-display] [data-timepicker-period-option="pm"]', 'aria-checked', 'true')
         ->click('#meeting-dialog [data-timepicker-label="hour12"][data-value="3"]')
         ->click('#meeting-dialog [data-timepicker-label="minute"][data-value="15"]')
         ->click('#meeting-dialog [data-timepicker-confirm]')
diff --git a/tests/Feature/Components/TimepickerTest.php b/tests/Feature/Components/TimepickerTest.php
index e80ba630..52725605 100644
--- a/tests/Feature/Components/TimepickerTest.php
+++ b/tests/Feature/Components/TimepickerTest.php
@@ -73,6 +73,12 @@ it('offers the input variant, the period selector and the actions', function ()
         ->toContain('data-timepicker-period-option="am"')
         ->toContain('data-timepicker-period-option="pm"')
         ->toContain('aria-label="Select AM or PM"')
+        // M3's labelling table: AM and PM are radios in a list, not toggle buttons.
+        ->toContain('role="radiogroup"')
+        ->toContain('role="radio"')
+        ->toContain('x-on:keydown.arrow-right.prevent="movePeriod($event)"')
+        // The 24-hour selector widens into the room the period selector leaves.
+        ->toContain('data-timepicker-display x-bind:data-cycle="is24 ? \'24\' : \'12\'"')
         ->toContain('aria-label="Switch to text input mode"')
         ->toContain('aria-label="Switch to clock mode"')
         ->toContain('data-timepicker-cancel')