diff --git a/src/k_battle.c b/src/k_battle.c
index e64fc5a9a..14ecfabf5 100644
--- a/src/k_battle.c
+++ b/src/k_battle.c
@@ -672,12 +672,11 @@ void K_RunBattleOvertime(void)
 
 	if (battleovertime.radius > 0)
 	{
-		const fixed_t pi = (22 * FRACUNIT) / 7; // loose approximation, this doesn't need to be incredibly precise
 		const INT32 orbs = 32;
 		const angle_t angoff = ANGLE_MAX / orbs;
 		const UINT8 spriteSpacing = 128;
 
-		fixed_t circumference = FixedMul(pi, battleovertime.radius * 2);
+		fixed_t circumference = FixedMul(M_PI_FIXED, battleovertime.radius * 2);
 		fixed_t scale = max(circumference / spriteSpacing / orbs, mapobjectscale);
 
 		fixed_t size = FixedMul(mobjinfo[MT_OVERTIME_PARTICLE].radius, scale);
diff --git a/src/k_follower.c b/src/k_follower.c
index 6b9b20c08..4d7556dd4 100644
--- a/src/k_follower.c
+++ b/src/k_follower.c
@@ -244,8 +244,7 @@ void K_HandleFollower(player_t *player)
 	// finally, add a cool floating effect to the z height.
 	// not stolen from k_kart I swear!!
 	{
-		const fixed_t pi = (22<<FRACBITS) / 7; // loose approximation, this doesn't need to be incredibly precise
-		fixed_t sine = FixedMul(fl.bobamp, FINESINE(((FixedMul(8 * pi, fl.bobspeed) * leveltime) >> ANGLETOFINESHIFT) & FINEMASK));
+		fixed_t sine = FixedMul(fl.bobamp, FINESINE(((FixedMul(4 * M_TAU_FIXED, fl.bobspeed) * leveltime) >> ANGLETOFINESHIFT) & FINEMASK));
 		sz += FixedMul(player->mo->scale, sine) * P_MobjFlip(player->mo);
 	}
 
diff --git a/src/k_kart.c b/src/k_kart.c
index e5fe76af1..42adaf268 100644
--- a/src/k_kart.c
+++ b/src/k_kart.c
@@ -6631,12 +6631,10 @@ static void K_MoveHeldObjects(player_t *player)
 					targy = player->mo->y + P_ReturnThrustY(cur, cur->angle + angoffset, cur->extravalue1);
 
 					{ // bobbing, copy pasted from my kimokawaiii entry
-						const fixed_t pi = (22<<FRACBITS) / 7; // loose approximation, this doesn't need to be incredibly precise
-						fixed_t sine = FixedMul(player->mo->scale, 8 * FINESINE((((2*pi*(4*TICRATE)) * leveltime)>>ANGLETOFINESHIFT) & FINEMASK));
+						fixed_t sine = FixedMul(player->mo->scale, 8 * FINESINE((((M_TAU_FIXED * (4*TICRATE)) * leveltime) >> ANGLETOFINESHIFT) & FINEMASK));
 						targz = (player->mo->z + (player->mo->height/2)) + sine;
 						if (player->mo->eflags & MFE_VERTICALFLIP)
 							targz += (player->mo->height/2 - 32*player->mo->scale)*6;
-
 					}
 
 					if (cur->tracer)
diff --git a/src/m_fixed.h b/src/m_fixed.h
index 49108ab93..9f3bb2910 100644
--- a/src/m_fixed.h
+++ b/src/m_fixed.h
@@ -37,6 +37,8 @@
 #define M_TAU_FIXED 411769
 #endif
 
+#define M_PI_FIXED (M_TAU_FIXED >> 1)
+
 typedef INT32 fixed_t;
 
 /*!
diff --git a/src/m_menu.c b/src/m_menu.c
index 63c5c2f7b..fcb2d6321 100644
--- a/src/m_menu.c
+++ b/src/m_menu.c
@@ -9666,9 +9666,9 @@ static void M_DrawSetupMultiPlayerMenu(void)
 
 			// Fake the follower's in game appearance by now also applying some of its variables! coolio, eh?
 			follower_t fl = followers[setupm_fakefollower];	// shortcut for our sanity
+
 			// smooth floating, totally not stolen from rocket sneakers.
-			const fixed_t pi = (22<<FRACBITS) / 7; // loose approximation, this doesn't need to be incredibly precise
-			fixed_t sine = FixedMul(fl.bobamp, FINESINE(((FixedMul(8 * pi, fl.bobspeed) * followertimer)>>ANGLETOFINESHIFT) & FINEMASK));
+			fixed_t sine = FixedMul(fl.bobamp, FINESINE(((FixedMul(4 * M_TAU_FIXED, fl.bobspeed) * followertimer)>>ANGLETOFINESHIFT) & FINEMASK));
 
 			UINT8 *colormap = R_GetTranslationColormap(TC_DEFAULT, setupm_fakecolor->color, 0); // why does GTC_MENUCACHE not work here...?
 			V_DrawFixedPatch((mx+65)*FRACUNIT, ((my+131)*FRACUNIT)-fl.zoffs+sine, fl.scale, flags, patch, colormap);
diff --git a/src/p_mobj.c b/src/p_mobj.c
index 433ff4931..e00d7ef2f 100644
--- a/src/p_mobj.c
+++ b/src/p_mobj.c
@@ -8597,8 +8597,7 @@ static boolean P_MobjRegularThink(mobj_t *mobj)
 			if (mobj->extravalue1)
 			{
 				const INT32 speed = 6*TICRATE; // longer is slower
-				const fixed_t pi = 22*FRACUNIT/7; // Inaccurate, but is close enough for our usage
-				fixed_t sine = FINESINE((((2*pi*speed) * leveltime) >> ANGLETOFINESHIFT) & FINEMASK) * flip;
+				fixed_t sine = FINESINE((((M_TAU_FIXED * speed) * leveltime) >> ANGLETOFINESHIFT) & FINEMASK) * flip;
 
 				// Flying capsules are flipped upside-down, like S3K
 				flip = -flip;